New statistical potential for quality assessment of protein models and a survey of energy functions

RNA 3D Structure Prediction: Progress and Perspective

Ribonucleic acid (RNA) molecules play vital roles in numerous important biological functions such as catalysis and gene regulation. The functions of RNAs are strongly coupled to their structures or proper structure changes, and RNA structure prediction has been paid much attention in the last two decades. Some computational models have been developed to predict RNA three-dimensional (3D) structures in silico, and these models are generally composed of predicting RNA 3D structure ensemble, evaluating near-native RNAs from the structure ensemble, and refining the identified RNAs. In this review, we will make a comprehensive overview of the recent advances in RNA 3D structure modeling, including structure ensemble prediction, evaluation, and refinement. Finally, we will emphasize some insights and perspectives in modeling RNA 3D structures.

cgRNASP: coarse-grained statistical potentials with residue separation for RNA structure evaluation

Knowledge-based statistical potentials are very important for RNA 3-dimensional (3D) structure prediction and evaluation. In recent years, various coarse-grained (CG) and all-atom models have been developed for predicting RNA 3D structures, while there is still lack of reliable CG statistical potentials not only for CG structure evaluation but also for all-atom structure evaluation at high efficiency. In this work, we have developed a series of residue-separation-based CG statistical potentials at different CG levels for RNA 3D structure evaluation, namely cgRNASP, which is composed of long-ranged and short-ranged interactions by residue separation. Compared with the newly developed all-atom rsRNASP, the short-ranged interaction in cgRNASP was involved more subtly and completely. Our examinations show that, the performance of cgRNASP varies with CG levels and compared with rsRNASP, cgRNASP has similarly good performance for extensive types of test datasets and can have slightly better performance for the realistic dataset-RNA-Puzzles dataset. Furthermore, cgRNASP is strikingly more efficient than all-atom statistical potentials/scoring functions, and can be apparently superior to other all-atom statistical potentials and scoring functions trained from neural networks for the RNA-Puzzles dataset. cgRNASP is available at https://github.com/Tan-group/cgRNASP.

ppdx: Automated modeling of protein-protein interaction descriptors for use with machine learning

This paper describes ppdx, a python workflow tool that combines protein sequence alignment, homology modeling, and structural refinement, to compute a broad array of descriptors for characterizing protein-protein interactions. The descriptors can be used to predict various properties of interest, such as protein-protein binding affinities, or inhibitory concentrations (IC₅₀ ), using approaches that range from simple regression to more complex machine learning models. The software is highly modular. It supports different protocols for generating structures, and 95 descriptors can be currently computed. More protocols and descriptors can be easily added. The implementation is highly parallel and can fully exploit the available cores in a single workstation, or multiple nodes on a supercomputer, allowing many systems to be analyzed simultaneously. As an illustrative application, ppdx is used to parametrize a model that predicts the IC₅₀ of a set of antigens and a class of antibodies directed to the influenza hemagglutinin stalk.

On the Rapid Calculation of Binding Affinities for Antigen and Antibody Design and Affinity Maturation Simulations

The accurate and efficient calculation of protein-protein binding affinities is an essential component in antibody and antigen design and optimization, and in computer modeling of antibody affinity maturation. Such calculations remain challenging despite advances in computer hardware and algorithms, primarily because proteins are flexible molecules, and thus, require explicit or implicit incorporation of multiple conformational states into the computational procedure. The astronomical size of the amino acid sequence space further compounds the challenge by requiring predictions to be computed within a short time so that many sequence variants can be tested. In this study, we compare three classes of methods for antibody/antigen (Ab/Ag) binding affinity calculations: (i) a method that relies on the physical separation of the Ab/Ag complex in equilibrium molecular dynamics (MD) simulations, (ii) a collection of 18 scoring functions that act on an ensemble of structures created using homology modeling software, and (iii) methods based on the molecular mechanics-generalized Born surface area (MM-GBSA) energy decomposition, in which the individual contributions of the energy terms are scaled to optimize agreement with the experiment. When applied to a set of 49 antibody mutations in two Ab/HIV gp120 complexes, all of the methods are found to have modest accuracy, with the highest Pearson correlations reaching about 0.6. In particular, the most computationally intensive method, i.e., MD simulation, did not outperform several scoring functions. The optimized energy decomposition methods provided marginally higher accuracy, but at the expense of requiring experimental data for parametrization. Within each method class, we examined the effect of the number of independent computational replicates, i.e., modeled structures or reinitialized MD simulations, on the prediction accuracy. We suggest using about ten modeled structures for scoring methods, and about five simulation replicates for MD simulations as a rule of thumb for obtaining reasonable convergence. We anticipate that our study will be a useful resource for practitioners working to incorporate binding affinity calculations within their protein design and optimization process.

Multiscale affinity maturation simulations to elicit broadly neutralizing antibodies against HIV

The design of vaccines against highly mutable pathogens, such as HIV and influenza, requires a detailed understanding of how the adaptive immune system responds to encountering multiple variant antigens (Ags). Here, we describe a multiscale model of B cell receptor (BCR) affinity maturation that employs actual BCR nucleotide sequences and treats BCR/Ag interactions in atomistic detail. We apply the model to simulate the maturation of a broadly neutralizing Ab (bnAb) against HIV. Starting from a germline precursor sequence of the VRC01 anti-HIV Ab, we simulate BCR evolution in response to different vaccination protocols and different Ags, which were previously designed by us. The simulation results provide qualitative guidelines for future vaccine design and reveal unique insights into bnAb evolution against the CD4 binding site of HIV. Our model makes possible direct comparisons of simulated BCR populations with results of deep sequencing data, which will be explored in future applications.

Vaccination has saved more lives than any other medical procedure. But, we do not have robust ways to develop vaccines against highly mutable pathogens. For example, there is no effective vaccine against HIV, and a universal vaccine against diverse strains of influenza is also not available. The development of immunization strategies to elicit antibodies that can neutralize diverse strains of highly mutable pathogens (so-called ‘broadly neutralizing antibodies’, or bnAbs) would enable the design of universal vaccines against such pathogens, as well as other viruses that may emerge in the future. In this paper, we present an agent-based model of affinity maturation–the Darwinian process by which antibodies evolve against a pathogen–that, for the first time, enables the in silico investigation of real germline nucleotide sequences of antibodies known to evolve into potent bnAbs, evolving against real amino acid sequences of HIV-based vaccine-candidate proteins. Our results provide new insights into bnAb evolution against HIV, and can be used to qualitatively guide the future design of vaccines against highly mutable pathogens.

Structure‐conditioned amino‐acid couplings: how contact geometry affects pairwise sequence preferences

Relating a protein's sequence to its conformation is a central challenge for both structure prediction and sequence design. Statistical contact potentials, as well as their more descriptive versions that account for side‐chain orientation and other geometric descriptors, have served as simplistic but useful means of representing second‐order contributions in sequence–structure relationships. Here we ask what happens when a pairwise potential is conditioned on the fully defined geometry of interacting backbones fragments. We show that the resulting structure‐conditioned coupling energies more accurately reflect pair preferences as a function of structural contexts. These structure‐conditioned energies more reliably encode native sequence information and more highly correlate with experimentally determined coupling energies. Clustering a database of interaction motifs by structure results in ensembles of similar energies and clustering them by energy results in ensembles of similar structures. By comparing many pairs of interaction motifs and showing that structural similarity and energetic similarity go hand‐in‐hand, we provide a tangible link between modular sequence and structure elements. This link is applicable to structural modeling, and we show that scoring CASP models with structured‐conditioned energies results in substantially higher correlation with structural quality than scoring the same models with a contact potential. We conclude that structure‐conditioned coupling energies are a good way to model the impact of interaction geometry on second‐order sequence preferences.

A novel algorithm for ranking RNA structure candidates

RNA research is advancing at an ever increasing pace. The newest and most state-of-the-art instruments and techniques have made possible the discoveries of new RNAs, and they have carried the field to new frontiers of disease research, vaccine development, therapeutics, and architectonics. Like proteins, RNAs show a marked relationship between structure and function. A deeper grasp of RNAs requires a finer understanding of their elaborate structures. In pursuit of this, cutting-edge experimental and computational structure-probing techniques output several candidate geometries for a given RNA, each of which is perfectly aligned with experimentally determined parameters. Identifying which structure is the most accurate, however, remains a major obstacle. In recent years, several algorithms have been developed for ranking candidate RNA structures in order from most to least probable, though their levels of accuracy and transparency leave room for improvement. Most recently, advances in both areas are demonstrated by rsRNASP, a novel algorithm proposed by Tan et al. rsRNASP is a residue-separation-based statistical potential for three-dimensional structure evaluation, and it outperforms the leading algorithms in the field.

rsRNASP: A residue-separation-based statistical potential for RNA 3D structure evaluation

Knowledge-based statistical potentials have been shown to be rather effective in protein 3-dimensional (3D) structure evaluation and prediction. Recently, several statistical potentials have been developed for RNA 3D structure evaluation, while their performances are either still at a low level for the test datasets from structure prediction models or dependent on the "black-box" process through neural networks. In this work, we have developed an all-atom distance-dependent statistical potential based on residue separation for RNA 3D structure evaluation, namely rsRNASP, which is composed of short- and long-ranged potentials distinguished by residue separation. The extensive examinations against available RNA test datasets show that rsRNASP has apparently higher performance than the existing statistical potentials for the realistic test datasets with large RNAs from structure prediction models, including the newly released RNA-Puzzles dataset, and is comparable to the existing top statistical potentials for the test datasets with small RNAs or near-native decoys. In addition, rsRNASP is superior to RNA3DCNN, a recently developed scoring function through 3D convolutional neural networks. rsRNASP and the relevant databases are available to the public.

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.

SPServer: split-statistical potentials for the analysis of protein structures and protein-protein interactions

BACKGROUND

Statistical potentials, also named knowledge-based potentials, are scoring functions derived from empirical data that can be used to evaluate the quality of protein folds and protein-protein interaction (PPI) structures. In previous works we decomposed the statistical potentials in different terms, named Split-Statistical Potentials, accounting for the type of amino acid pairs, their hydrophobicity, solvent accessibility and type of secondary structure. These potentials have been successfully used to identify near-native structures in protein structure prediction, rank protein docking poses, and predict PPI binding affinities.

RESULTS

Here, we present the SPServer, a web server that applies the Split-Statistical Potentials to analyze protein folds and protein interfaces. SPServer provides global scores as well as residue/residue-pair profiles presented as score plots and maps. This level of detail allows users to: (1) identify potentially problematic regions on protein structures; (2) identify disrupting amino acid pairs in protein interfaces; and (3) compare and analyze the quality of tertiary and quaternary structural models.

CONCLUSIONS

While there are many web servers that provide scoring functions to assess the quality of either protein folds or PPI structures, SPServer integrates both aspects in a unique easy-to-use web server. Moreover, the server permits to locally assess the quality of the structures and interfaces at a residue level and provides tools to compare the local assessment between structures. SERVER ADDRESS: https://sbi.upf.edu/spserver/ .

A knowledge-based scoring function to assess quaternary associations of proteins

MOTIVATION

The elucidation of all inter-protein interactions would significantly enhance our knowledge of cellular processes at a molecular level. Given the enormity of the problem, the expenses and limitations of experimental methods, it is imperative that this problem is tackled computationally. In silico predictions of protein interactions entail sampling different conformations of the purported complex and then scoring these to assess for interaction viability. In this study, we have devised a new scheme for scoring protein-protein interactions.

RESULTS

Our method, PIZSA (Protein Interaction Z-Score Assessment), is a binary classification scheme for identification of native protein quaternary assemblies (binders/nonbinders) based on statistical potentials. The scoring scheme incorporates residue-residue contact preference on the interface with per residue-pair atomic contributions and accounts for clashes. PIZSA can accurately discriminate between native and non-native structural conformations from protein docking experiments and outperform other contact-based potential scoring functions. The method has been extensively benchmarked and is among the top 6 methods, outperforming 31 other statistical, physics based and machine learning scoring schemes. The PIZSA potentials can also distinguish crystallization artifacts from biological interactions.

AVAILABILITY AND IMPLEMENTATION

PIZSA is implemented as a web server at http://cospi.iiserpune.ac.in/pizsa and can be downloaded as a standalone package from http://cospi.iiserpune.ac.in/pizsa/Download/Download.html.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Revisiting the "satisfaction of spatial restraints" approach of MODELLER for protein homology modeling

The most frequently used approach for protein structure prediction is currently homology modeling. The 3D model building phase of this methodology is critical for obtaining an accurate and biologically useful prediction. The most widely employed tool to perform this task is MODELLER. This program implements the “modeling by satisfaction of spatial restraints” strategy and its core algorithm has not been altered significantly since the early 1990s. In this work, we have explored the idea of modifying MODELLER with two effective, yet computationally light strategies to improve its 3D modeling performance. Firstly, we have investigated how the level of accuracy in the estimation of structural variability between a target protein and its templates in the form of σ values profoundly influences 3D modeling. We show that the σ values produced by MODELLER are on average weakly correlated to the true level of structural divergence between target-template pairs and that increasing this correlation greatly improves the program’s predictions, especially in multiple-template modeling. Secondly, we have inquired into how the incorporation of statistical potential terms (such as the DOPE potential) in the MODELLER’s objective function impacts positively 3D modeling quality by providing a small but consistent improvement in metrics such as GDT-HA and lDDT and a large increase in stereochemical quality. Python modules to harness this second strategy are freely available at https://github.com/pymodproject/altmod. In summary, we show that there is a large room for improving MODELLER in terms of 3D modeling quality and we propose strategies that could be pursued in order to further increase its performance.

Proteins are fundamental biological molecules that carry out countless activities in living beings. Since the function of proteins is dictated by their three-dimensional atomic structures, acquiring structural details of proteins provides deep insights into their function. Currently, the most frequently used computational approach for protein structure prediction is template-based modeling. In this approach, a target protein is modeled using the experimentally-derived structural information of a template protein assumed to have a similar structure to the target. MODELLER is the most frequently used program for template-based 3D model building. Despite its success, its predictions are not always accurate enough to be useful in Biomedical Research. Here, we show that it is possible to greatly increase the performance of MODELLER by modifying two aspects of its algorithm. First, we demonstrate that providing the program with accurate estimations of local target-template structural divergence greatly increases the quality of its predictions. Additionally, we show that modifying MODELLER’s scoring function with statistical potential energetic terms also helps to improve modeling quality. This work will be useful in future research, since it reports practical strategies to improve the performance of this core tool in Structural Bioinformatics.

Assessment of chemical-crosslink-assisted protein structure modeling in CASP13

With the advance of experimental procedures obtaining chemical crosslinking information is becoming a fast and routine practice. Information on crosslinks can greatly enhance the accuracy of protein structure modeling. Here, we review the current state of the art in modeling protein structures with the assistance of experimentally determined chemical crosslinks within the framework of the 13th meeting of Critical Assessment of Structure Prediction approaches. This largest-to-date blind assessment reveals benefits of using data assistance in difficult to model protein structure prediction cases. However, in a broader context, it also suggests that with the unprecedented advance in accuracy to predict contacts in recent years, experimental crosslinks will be useful only if their specificity and accuracy further improved and they are better integrated into computational workflows.

A simple neural network implementation of generalized solvation free energy for assessment of protein structural models

Rapid and accurate assessment of protein structural models is essential for protein structure prediction and design. Great progress has been made in this regard, especially by recent application of "knowledge-based" potentials. Various machine learning based protein structural model quality assessment methods are also quite successful. However, performance of traditional "physics-based" models has not been as effective. Based on our analysis of the fundamental computational limitation behind unsatisfactory performance of "physics-based" models, we propose a generalized solvation free energy (GSFE) framework, which is intrinsically flexible for multi-scale treatments and is amenable for machine learning implementation. Finally, we implemented a simple example of backbone-based residue level GSFE with neural network, which was found to have competitive performance when compared with highly complex latest "knowledge-based" atomic potentials in distinguishing native structures from decoys.

Purely Structural Protein Scoring Functions Using Support Vector Machine and Ensemble Learning

The function of a protein is determined by its structure, which creates a need for efficient methods of protein structure determination to advance scientific and medical research. Because current experimental structure determination methods carry a high price tag, computational predictions are highly desirable. Given a protein sequence, computational methods produce numerous 3D structures known as decoys. Selection of the best quality decoys is both challenging and essential as the end users can handle only a few ones. Therefore, scoring functions are central to decoy selection. They combine measurable features into a single number indicator of decoy quality. Unfortunately, current scoring functions do not consistently select the best decoys. Machine learning techniques offer great potential to improve decoy scoring. This paper presents two machine-learning based scoring functions to predict the quality of proteins structures, i.e., the similarity between the predicted structure and the experimental one without knowing the latter. We use different metrics to compare these scoring functions against three state-of-the-art scores. This is a first attempt at comparing different scoring functions using the same non-redundant dataset for training and testing and the same features. The results show that adding informative features may be more significant than the method used.

ANDIS: an atomic angle- and distance-dependent statistical potential for protein structure quality assessment

Background

The knowledge-based statistical potential has been widely used in protein structure modeling and model quality assessment. They are commonly evaluated based on their abilities of native recognition as well as decoy discrimination. However, these two aspects are found to be mutually exclusive in many statistical potentials.

Results

We developed an atomic ANgle- and DIStance-dependent (ANDIS) statistical potential for protein structure quality assessment with distance cutoff being a tunable parameter. When distance cutoff is ≤9.0 Å, “effective atomic interaction” is employed to enhance the ability of native recognition. For a distance cutoff of ≥10 Å, the distance-dependent atom-pair potential with random-walk reference state is combined to strengthen the ability of decoy discrimination. Benchmark tests on 632 structural decoy sets from diverse sources demonstrate that ANDIS outperforms other state-of-the-art potentials in both native recognition and decoy discrimination.

Conclusions

Distance cutoff is a crucial parameter for distance-dependent statistical potentials. A lower distance cutoff is better for native recognition, while a higher one is favorable for decoy discrimination. The ANDIS potential is freely available as a standalone application at http://qbp.hzau.edu.cn/ANDIS/.

Electronic supplementary material

The online version of this article (10.1186/s12859-019-2898-y) contains supplementary material, which is available to authorized users.

Methods for the Refinement of Protein Structure 3D Models

The refinement of predicted 3D protein models is crucial in bringing them closer towards experimental accuracy for further computational studies. Refinement approaches can be divided into two main stages: The sampling and scoring stages. Sampling strategies, such as the popular Molecular Dynamics (MD)-based protocols, aim to generate improved 3D models. However, generating 3D models that are closer to the native structure than the initial model remains challenging, as structural deviations from the native basin can be encountered due to force-field inaccuracies. Therefore, different restraint strategies have been applied in order to avoid deviations away from the native structure. For example, the accurate prediction of local errors and/or contacts in the initial models can be used to guide restraints. MD-based protocols, using physics-based force fields and smart restraints, have made significant progress towards a more consistent refinement of 3D models. The scoring stage, including energy functions and Model Quality Assessment Programs (MQAPs) are also used to discriminate near-native conformations from non-native conformations. Nevertheless, there are often very small differences among generated 3D models in refinement pipelines, which makes model discrimination and selection problematic. For this reason, the identification of the most native-like conformations remains a major challenge.

Toward a unified scoring function for native state discrimination and drug-binding pocket recognition

Protein folding and receptor-ligand recognition are fundamental processes for any living organism. Although folding and ligand recognition are based on the same chemistry, the existing empirical scoring functions target just one problem: predicting the correct fold or the correct binding pose. We here introduce a statistical potential which considers moieties as fundamental units. The scoring function is able to deal with both folding and ligand pocket recognition problems with a performance comparable to the scoring functions specifically tailored for one of the two tasks. We foresee that the capability of the new scoring function to tackle both problems in a unified framework will be a key to deal with the induced fit phenomena, in which a target protein changes significantly its conformation upon binding. Moreover, the new scoring function might be useful in docking protocols towards intrinsically disordered proteins, whose flexibility cannot be handled with the available docking software.

Estimation of the breadth of CD4bs targeting HIV antibodies by molecular modeling and machine learning

HIV is a highly mutable virus for which all attempts to develop a vaccine have been unsuccessful. Nevertheless, few long-infected patients develop antibodies, called broadly neutralizing antibodies (bnAbs), that have a high breadth and can neutralize multiple variants of the virus. This suggests that a universal HIV vaccine should be possible. A measure of the efficacy of a HIV vaccine is the neutralization breadth of the antibodies it generates. The breadth is defined as the fraction of viruses in the Seaman panel that are neutralized by the antibody. Experimentally the neutralization ability is measured as the half maximal inhibitory concentration of the antibody (IC50). To avoid such time-consuming experimental measurements, we developed a computational approach to estimate the IC50 and use it to determine the antibody breadth. Given that no direct method exists for calculating IC50 values, we resort to a combination of atomistic modeling and machine learning. For each antibody/virus complex, an all-atoms model is built using the amino acid sequence and a known structure of a related complex. Then a series of descriptors are derived from the atomistic models, and these are used to train a Multi-Layer Perceptron (an Artificial Neural Network) to predict the value of the IC50 (by regression), or if the antibody binds or not to the virus (by classification). The neural networks are trained by use of experimental IC50 values collected in the CATNAP database. The computed breadths obtained by regression and classification are reported and the importance of having some related information in the data set for obtaining accurate predictions is analyzed. This approach is expected to prove useful for the design of HIV bnAbs, where the computation of the potency must be accompanied by a computation of the breadth, and for evaluating the efficiency of potential vaccination schemes developed through modeling and simulation.

Contact Potential for Structure Prediction of Proteins and Protein Complexes from Potts Model

The energy function is the key component of protein modeling methodology. This work presents a semianalytical approach to the development of contact potentials for protein structure modeling. Residue-residue and atom-atom contact energies were derived by maximizing the probability of observing native sequences in a nonredundant set of protein structures. The optimization task was formulated as an inverse statistical mechanics problem applied to the Potts model. Its solution by pseudolikelihood maximization provides consistent estimates of coupling constants at atomic and residue levels. The best performance was achieved when interacting atoms were grouped according to their physicochemical properties. For individual protein structures, the performance of the contact potentials in distinguishing near-native structures from the decoys is similar to the top-performing scoring functions. The potentials also yielded significant improvement in the protein docking success rates. The potentials recapitulated experimentally determined protein stability changes upon point mutations and protein-protein binding affinities. The approach offers a different perspective on knowledge-based potentials and may serve as the basis for their further development.

Protein structure prediction

Predicting 3D structure of protein from its amino acid sequence is one of the most important unsolved problems in biophysics and computational biology. This paper attempts to give a comprehensive introduction of the most recent effort and progress on protein structure prediction. Following the general flowchart of structure prediction, related concepts and methods are presented and discussed. Moreover, brief introductions are made to several widely-used prediction methods and the community-wide critical assessment of protein structure prediction (CASP) experiments.

All-Atom Four-Body Knowledge-Based Statistical Potentials to Distinguish Native Protein Structures from Nonnative Folds

Recent advances in understanding protein folding have benefitted from coarse-grained representations of protein structures. Empirical energy functions derived from these techniques occasionally succeed in distinguishing native structures from their corresponding ensembles of nonnative folds or decoys which display varying degrees of structural dissimilarity to the native proteins. Here we utilized atomic coordinates of single protein chains, comprising a large diverse training set, to develop and evaluate twelve all-atom four-body statistical potentials obtained by exploring alternative values for a pair of inherent parameters. Delaunay tessellation was performed on the atomic coordinates of each protein to objectively identify all quadruplets of interacting atoms, and atomic potentials were generated via statistical analysis of the data and implementation of the inverted Boltzmann principle. Our potentials were evaluated using benchmarking datasets from Decoys-‘R'-Us, and comparisons were made with twelve other physics- and knowledge-based potentials. Ranking 3rd, our best potential tied CHARMM19 and surpassed AMBER force field potentials. We illustrate how a generalized version of our potential can be used to empirically calculate binding energies for target-ligand complexes, using HIV-1 protease-inhibitor complexes for a practical application. The combined results suggest an accurate and efficient atomic four-body statistical potential for protein structure prediction and assessment.

Computational protein structure refinement: Almost there, yet still so far to go

Protein structures are essential in modern biology yet experimental methods are far from being able to catch up with the rapid increase in available genomic data. Computational protein structure prediction methods aim to fill the gap while the role of protein structure refinement is to take approximate initial template-based models and bring them closer to the true native structure. Current methods for computational structure refinement rely on molecular dynamics simulations, related sampling methods, or iterative structure optimization protocols. The best methods are able to achieve moderate degrees of refinement but consistent refinement that can reach near-experimental accuracy remains elusive. Key issues revolve around the accuracy of the energy function, the inability to reliably rank multiple models, and the use of restraints that keep sampling close to the native state but also limit the degree of possible refinement. A different aspect is the question of what exactly the target of high-resolution refinement should be as experimental structures are affected by experimental conditions and different biological questions require varying levels of accuracy. While improvement of the global protein structure is a difficult problem, high-resolution refinement methods that improves local structural quality such as favorable stereochemistry and the avoidance of atomic clashes are much more successful.

Knowledge-based entropies improve the identification of native protein structures

Evaluating protein structures requires reliable free energies with good estimates of both potential energies and entropies. Although there are many demonstrated successes from using knowledge-based potential energies, computing entropies of proteins has lagged far behind. Here we take an entirely different approach and evaluate knowledge-based conformational entropies of proteins based on the observed frequencies of contact changes between amino acids in a set of 167 diverse proteins, each of which has two alternative structures. The results show that charged and polar interactions break more often than hydrophobic pairs. This pattern correlates strongly with the average solvent exposure of amino acids in globular proteins, as well as with polarity indices and the sizes of the amino acids. Knowledge-based entropies are derived by using the inverse Boltzmann relationship, in a manner analogous to the way that knowledge-based potentials have been extracted. Including these new knowledge-based entropies almost doubles the performance of knowledge-based potentials in selecting the native protein structures from decoy sets. Beyond the overall energy-entropy compensation, a similar compensation is seen for individual pairs of interacting amino acids. The entropies in this report have immediate applications for 3D structure prediction, protein model assessment, and protein engineering and design.

An Atomistic Statistically Effective Energy Function for Computational Protein Design

Shortcomings in the definition of effective free-energy surfaces of proteins are recognized to be a major contributory factor responsible for the low success rates of existing automated methods for computational protein design (CPD). The formulation of an atomistic statistically effective energy function (SEEF) suitable for a wide range of CPD applications and its derivation from structural data extracted from protein domains and protein-ligand complexes are described here. The proposed energy function comprises nonlocal atom-based and local residue-based SEEFs, which are coupled using a novel atom connectivity number factor to scale short-range, pairwise, nonbonded atomic interaction energies and a surface-area-dependent cavity energy term. This energy function was used to derive additional SEEFs describing the unfolded-state ensemble of any given residue sequence based on computed average energies for partially or fully solvent-exposed fragments in regions of irregular structure in native proteins. Relative thermal stabilities of 97 T4 bacteriophage lysozyme mutants were predicted from calculated energy differences for folded and unfolded states with an average unsigned error (AUE) of 0.84 kcal mol(-1) when compared to experiment. To demonstrate the utility of the energy function for CPD, further validation was carried out in tests of its capacity to recover cognate protein sequences and to discriminate native and near-native protein folds, loop conformers, and small-molecule ligand binding poses from non-native benchmark decoys. Experimental ligand binding free energies for a diverse set of 80 protein complexes could be predicted with an AUE of 2.4 kcal mol(-1) using an additional energy term to account for the loss in ligand configurational entropy upon binding. The atomistic SEEF is expected to improve the accuracy of residue-based coarse-grained SEEFs currently used in CPD and to extend the range of applications of extant atom-based protein statistical potentials.

Predicting the Effect of Mutations on Protein-Protein Binding Interactions through Structure-Based Interface Profiles

The formation of protein-protein complexes is essential for proteins to perform their physiological functions in the cell. Mutations that prevent the proper formation of the correct complexes can have serious consequences for the associated cellular processes. Since experimental determination of protein-protein binding affinity remains difficult when performed on a large scale, computational methods for predicting the consequences of mutations on binding affinity are highly desirable. We show that a scoring function based on interface structure profiles collected from analogous protein-protein interactions in the PDB is a powerful predictor of protein binding affinity changes upon mutation. As a standalone feature, the differences between the interface profile score of the mutant and wild-type proteins has an accuracy equivalent to the best all-atom potentials, despite being two orders of magnitude faster once the profile has been constructed. Due to its unique sensitivity in collecting the evolutionary profiles of analogous binding interactions and the high speed of calculation, the interface profile score has additional advantages as a complementary feature to combine with physics-based potentials for improving the accuracy of composite scoring approaches. By incorporating the sequence-derived and residue-level coarse-grained potentials with the interface structure profile score, a composite model was constructed through the random forest training, which generates a Pearson correlation coefficient >0.8 between the predicted and observed binding free-energy changes upon mutation. This accuracy is comparable to, or outperforms in most cases, the current best methods, but does not require high-resolution full-atomic models of the mutant structures. The binding interface profiling approach should find useful application in human-disease mutation recognition and protein interface design studies.

Few proteins carry out their tasks in isolation. Instead, proteins combine with each other in complicated ways that can be affected by either the natural genetic variation that occurs among people or by disease causing mutations such as those that occur in cancer or in genetic disorders. To understand how these mutations affect our health, it is necessary to understand how mutations can affect the strength of the interactions that bind proteins together. This is a difficult task to do in a laboratory on a large scale and scientists are increasingly turning to computational methods to predict these effects in advance. We show that by looking at the multiple alignments of similar protein-protein complex structures at the interface regions, new constraints based on the evolution of the three dimensional structures of proteins can be made to predict which mutations are compatible with two proteins interacting and which are not.

Protein structure prediction using residue- and fragment-environment potentials in CASP11

An accurate scoring function that can select near-native structure models from a pool of alternative models is key for successful protein structure prediction. For the critical assessment of techniques for protein structure prediction (CASP) 11, we have built a protocol of protein structure prediction that has novel coarse-grained scoring functions for selecting decoys as the heart of its pipeline. The score named PRESCO (Protein Residue Environment SCOre) developed recently by our group evaluates the native-likeness of local structural environment of residues in a structure decoy considering positions and the depth of side-chains of spatially neighboring residues. We also introduced a helix interaction potential as an additional scoring function for selecting decoys. The best models selected by PRESCO and the helix interaction potential underwent structure refinement, which includes side-chain modeling and relaxation with a short molecular dynamics simulation. Our protocol was successful, achieving the top rank in the free modeling category with a significant margin of the accumulated Z-score to the subsequent groups when the top 1 models were considered. Proteins 2016; 84(Suppl 1):105-117. © 2015 Wiley Periodicals, Inc.

Modularity of Protein Folds as a Tool for Template-Free Modeling of Structures

Predicting the three-dimensional structure of proteins from their amino acid sequences remains a challenging problem in molecular biology. While the current structural coverage of proteins is almost exclusively provided by template-based techniques, the modeling of the rest of the protein sequences increasingly require template-free methods. However, template-free modeling methods are much less reliable and are usually applicable for smaller proteins, leaving much space for improvement. We present here a novel computational method that uses a library of supersecondary structure fragments, known as Smotifs, to model protein structures. The library of Smotifs has saturated over time, providing a theoretical foundation for efficient modeling. The method relies on weak sequence signals from remotely related protein structures to create a library of Smotif fragments specific to the target protein sequence. This Smotif library is exploited in a fragment assembly protocol to sample decoys, which are assessed by a composite scoring function. Since the Smotif fragments are larger in size compared to the ones used in other fragment-based methods, the proposed modeling algorithm, SmotifTF, can employ an exhaustive sampling during decoy assembly. SmotifTF successfully predicts the overall fold of the target proteins in about 50% of the test cases and performs competitively when compared to other state of the art prediction methods, especially when sequence signal to remote homologs is diminishing. Smotif-based modeling is complementary to current prediction methods and provides a promising direction in addressing the structure prediction problem, especially when targeting larger proteins for modeling.

Each protein folds into a unique three-dimensional structure that enables it to carry out its biological function. Knowledge of the atomic details of protein structures is therefore a key to understanding their function. Advances in high throughput experimental technologies have lead to an exponential increase in the availability of known protein sequences. Although strong progress has been made in experimental protein structure determination, it remains a fact that more than 99% of structural information is provided by computational modeling methods. We describe here a novel structure prediction method, SmotifTF, which uses a unique library of known protein fragments to assemble the three-dimensional structure of a sequence. The fragment library has saturated over time and therefore provides a complete set of building blocks required for model building. The method performs competitively compared to existing methods of structure prediction.

StaRProtein, a web server for prediction of the stability of repeat proteins

Repeat proteins have become increasingly important due to their capability to bind to almost any proteins and the potential as alternative therapy to monoclonal antibodies. In the past decade repeat proteins have been designed to mediate specific protein-protein interactions. The tetratricopeptide and ankyrin repeat proteins are two classes of helical repeat proteins that form different binding pockets to accommodate various partners. It is important to understand the factors that define folding and stability of repeat proteins in order to prioritize the most stable designed repeat proteins to further explore their potential binding affinities. Here we developed distance-dependant statistical potentials using two classes of alpha-helical repeat proteins, tetratricopeptide and ankyrin repeat proteins respectively, and evaluated their efficiency in predicting the stability of repeat proteins. We demonstrated that the repeat-specific statistical potentials based on these two classes of repeat proteins showed paramount accuracy compared with non-specific statistical potentials in: 1) discriminate correct vs. incorrect models 2) rank the stability of designed repeat proteins. In particular, the statistical scores correlate closely with the equilibrium unfolding free energies of repeat proteins and therefore would serve as a novel tool in quickly prioritizing the designed repeat proteins with high stability. StaRProtein web server was developed for predicting the stability of repeat proteins.

Optimized distance-dependent atom-pair-based potential DOOP for protein structure prediction

The DOcking decoy-based Optimized Potential (DOOP) energy function for protein structure prediction is based on empirical distance-dependent atom-pair interactions. To optimize the atom-pair interactions, native protein structures are decomposed into polypeptide chain segments that correspond to structural motives involving complete secondary structure elements. They constitute near native ligand-receptor systems (or just pairs). Thus, a total of 8609 ligand-receptor systems were prepared from 954 selected proteins. For each of these hypothetical ligand-receptor systems, 1000 evenly sampled docking decoys with 0-10 Å interface root-mean-square-deviation (iRMSD) were generated with a method used before for protein-protein docking. A neural network-based optimization method was applied to derive the optimized energy parameters using these decoys so that the energy function mimics the funnel-like energy landscape for the interaction between these hypothetical ligand-receptor systems. Thus, our method hierarchically models the overall funnel-like energy landscape of native protein structures. The resulting energy function was tested on several commonly used decoy sets for native protein structure recognition and compared with other statistical potentials. In combination with a torsion potential term which describes the local conformational preference, the atom-pair-based potential outperforms other reported statistical energy functions in correct ranking of native protein structures for a variety of decoy sets. This is especially the case for the most challenging ROSETTA decoy set, although it does not take into account side chain orientation-dependence explicitly. The DOOP energy function for protein structure prediction, the underlying database of protein structures with hypothetical ligand-receptor systems and their decoys are freely available at http://agknapp.chemie.fu-berlin.de/doop/.

Bhageerath-H: a homology/ab initio hybrid server for predicting tertiary structures of monomeric soluble proteins

BACKGROUND

The advent of human genome sequencing project has led to a spurt in the number of protein sequences in the databanks. Success of structure based drug discovery severely hinges on the availability of structures. Despite significant progresses in the area of experimental protein structure determination, the sequence-structure gap is continually widening. Data driven homology based computational methods have proved successful in predicting tertiary structures for sequences sharing medium to high sequence similarities. With dwindling similarities of query sequences, advanced homology/ ab initio hybrid approaches are being explored to solve structure prediction problem. Here we describe Bhageerath-H, a homology/ ab initio hybrid software/server for predicting protein tertiary structures with advancing drug design attempts as one of the goals.

RESULTS

Bhageerath-H web-server was validated on 75 CASP10 targets which showed TM-scores ≥ 0.5 in 91% of the cases and Cα RMSDs ≤ 5 Å from the native in 58% of the targets, which is well above the CASP10 water mark. Comparison with some leading servers demonstrated the uniqueness of the hybrid methodology in effectively sampling conformational space, scoring best decoys and refining low resolution models to high and medium resolution.

CONCLUSION

Bhageerath-H methodology is web enabled for the scientific community as a freely accessible web server. The methodology is fielded in the on-going CASP11 experiment.

Detecting local residue environment similarity for recognizing near-native structure models

We developed a new representation of local amino acid environments in protein structures called the Side-chain Depth Environment (SDE). An SDE defines a local structural environment of a residue considering the coordinates and the depth of amino acids that locate in the vicinity of the side-chain centroid of the residue. SDEs are general enough that similar SDEs are found in protein structures with globally different folds. Using SDEs, we developed a procedure called PRESCO (Protein Residue Environment SCOre) for selecting native or near-native models from a pool of computational models. The procedure searches similar residue environments observed in a query model against a set of representative native protein structures to quantify how native-like SDEs in the model are. When benchmarked on commonly used computational model datasets, our PRESCO compared favorably with the other existing scoring functions in selecting native and near-native models.

ROTAS: a rotamer-dependent, atomic statistical potential for assessment and prediction of protein structures

Background

Multibody potentials accounting for cooperative effects of molecular interactions have shown better accuracy than typical pairwise potentials. The main challenge in the development of such potentials is to find relevant structural features that characterize the tightly folded proteins. Also, the side-chains of residues adopt several specific, staggered conformations, known as rotamers within protein structures. Different molecular conformations result in different dipole moments and induce charge reorientations. However, until now modeling of the rotameric state of residues had not been incorporated into the development of multibody potentials for modeling non-bonded interactions in protein structures.

Results

In this study, we develop a new multibody statistical potential which can account for the influence of rotameric states on the specificity of atomic interactions. In this potential, named “rotamer-dependent atomic statistical potential” (ROTAS), the interaction between two atoms is specified by not only the distance and relative orientation but also by two state parameters concerning the rotameric state of the residues to which the interacting atoms belong. It was clearly found that the rotameric state is correlated to the specificity of atomic interactions. Such rotamer-dependencies are not limited to specific type or certain range of interactions. The performance of ROTAS was tested using 13 sets of decoys and was compared to those of existing atomic-level statistical potentials which incorporate orientation-dependent energy terms. The results show that ROTAS performs better than other competing potentials not only in native structure recognition, but also in best model selection and correlation coefficients between energy and model quality.

Conclusions

A new multibody statistical potential, ROTAS accounting for the influence of rotameric states on the specificity of atomic interactions was developed and tested on decoy sets. The results show that ROTAS has improved ability to recognize native structure from decoy models compared to other potentials. The effectiveness of ROTAS may provide insightful information for the development of many applications which require accurate side-chain modeling such as protein design, mutation analysis, and docking simulation.

Electronic supplementary material

The online version of this article (doi:10.1186/1471-2105-15-307) contains supplementary material, which is available to authorized users.

Smotifs as structural local descriptors of supersecondary elements: classification, completeness and applications

Protein structures are made up of periodic and aperiodic structural elements (i.e., α-helices, β-strands and loops). Despite the apparent lack of regular structure, loops have specific conformations and play a central role in the folding, dynamics, and function of proteins. In this article, we reviewed our previous works in the study of protein loops as local supersecondary structural motifs or Smotifs. We reexamined our works about the structural classification of loops (ArchDB) and its application to loop structure prediction (ArchPRED), including the assessment of the limits of knowledge-based loop structure prediction methods. We finalized this article by focusing on the modular nature of proteins and how the concept of Smotifs provides a convenient and practical approach to decompose proteins into strings of concatenated Smotifs and how can this be used in computational protein design and protein structure prediction.

Optimized atomic statistical potentials: assessment of protein interfaces and loops

MOTIVATION

Statistical potentials have been widely used for modeling whole proteins and their parts (e.g. sidechains and loops) as well as interactions between proteins, nucleic acids and small molecules. Here, we formulate the statistical potentials entirely within a statistical framework, avoiding questionable statistical mechanical assumptions and approximations, including a definition of the reference state.

RESULTS

We derive a general Bayesian framework for inferring statistically optimized atomic potentials (SOAP) in which the reference state is replaced with data-driven 'recovery' functions. Moreover, we restrain the relative orientation between two covalent bonds instead of a simple distance between two atoms, in an effort to capture orientation-dependent interactions such as hydrogen bonds. To demonstrate this general approach, we computed statistical potentials for protein-protein docking (SOAP-PP) and loop modeling (SOAP-Loop). For docking, a near-native model is within the top 10 scoring models in 40% of the PatchDock benchmark cases, compared with 23 and 27% for the state-of-the-art ZDOCK and FireDock scoring functions, respectively. Similarly, for modeling 12-residue loops in the PLOP benchmark, the average main-chain root mean square deviation of the best scored conformations by SOAP-Loop is 1.5 Å, close to the average root mean square deviation of the best sampled conformations (1.2 Å) and significantly better than that selected by Rosetta (2.1 Å), DFIRE (2.3 Å), DOPE (2.5 Å) and PLOP scoring functions (3.0 Å). Our Bayesian framework may also result in more accurate statistical potentials for additional modeling applications, thus affording better leverage of the experimentally determined protein structures.

AVAILABILITY AND IMPLEMENTATION

SOAP-PP and SOAP-Loop are available as part of MODELLER (http://salilab.org/modeller).

Using the unfolded state as the reference state improves the performance of statistical potentials

Distance-dependent statistical potentials are an important class of energy functions extensively used in modeling protein structures and energetics. These potentials are obtained by statistically analyzing the proximity of atoms in all combinatorial amino-acid pairs in proteins with known structures. In model evaluation, the statistical potential is usually subtracted by the value of a reference state for better selectivity. An ideal reference state should include the general chemical properties of polypeptide chains so that only the unique factors stabilizing the native structures are retained after calibrating on reference state. However, reference states available as of this writing rarely model specific chemical constraints of peptide bonds and therefore poorly reflect the behavior of polypeptide chains. In this work, we proposed a statistical potential based on unfolded state ensemble (SPOUSE), where the reference state is summarized from the unfolded state ensembles of proteins produced according to the statistical coil model. Due to its better representation of the features of polypeptides, SPOUSE outperforms three of the most widely used distance-dependent potentials not only in native conformation identification, but also in the selection of close-to-native models and correlation coefficients between energy and model error. Furthermore, SPOUSE shows promising possibility of further improvement by integration with the orientation-dependent side-chain potentials.

Modeling proteins using a super-secondary structure library and NMR chemical shift information

A remaining challenge in protein modeling is to predict structures for sequences with no sequence similarity to any experimentally solved structure. Based on earlier observations, the library of protein backbone supersecondary structure motifs (Smotifs) saturated about a decade ago. Therefore, it should be possible to build any structure from a combination of existing Smotifs with the help of limited experimental data that are sufficient to relate the backbone conformations of Smotifs between target proteins and known structures. Here, we present a hybrid modeling algorithm that relies on an exhaustive Smotif library and on nuclear magnetic resonance chemical shift patterns without any input of primary sequence information. In a test of 102 proteins, the algorithm delivered 90 homology-model-quality models, among them 24 high-quality ones, and a topologically correct solution for almost all cases. The current approach opens a venue to address the modeling of larger protein structures for which chemical shifts are available.

Capturing native/native like structures with a physico-chemical metric (pcSM) in protein folding

Specification of the three dimensional structure of a protein from its amino acid sequence, also called a "Grand Challenge" problem, has eluded a solution for over six decades. A modestly successful strategy has evolved over the last couple of decades based on development of scoring functions (e.g. mimicking free energy) that can capture native or native-like structures from an ensemble of decoys generated as plausible candidates for the native structure. A scoring function must be fast enough in discriminating the native from unfolded/misfolded structures, and requires validation on a large data set(s) to generate sufficient confidence in the score. Here we develop a scoring function called pcSM that detects true native structure in the top 5 with 93% accuracy from an ensemble of candidate structures. If we eliminate the native from ensemble of decoys then pcSM is able to capture near native structure (RMSD<=5Ǻ) in top 10 with 86% accuracy. The parameters considered in pcSM are a C-alpha Euclidean metric, secondary structural propensity, surface areas and an intramolecular energy function. pcSM has been tested on 415 systems consisting 142,698 decoys (public and CASP-largest reported hitherto in literature). The average rank for the native is 2.38, a significant improvement over that existing in literature. In-silico protein structure prediction requires robust scoring technique(s). Therefore, pcSM is easily amenable to integration into a successful protein structure prediction strategy. The tool is freely available at http://www.scfbio-iitd.res.in/software/pcsm.jsp.