Protein model refinement using an optimized physics-based all-atom force field

Using Local Protein Model Quality Estimates to Guide a Molecular Dynamics-Based Refinement Strategy

The refinement of predicted 3D models aims to bring them closer to the native structure by fixing errors including unusual bonds and torsion angles and irregular hydrogen bonding patterns. Refinement approaches based on molecular dynamics (MD) simulations using different types of restraints have performed well since CASP10. ReFOLD, developed by the McGuffin group, was one of the many MD-based refinement approaches, which were tested in CASP 12. When the performance of the ReFOLD method in CASP12 was evaluated, it was observed that ReFOLD suffered from the absence of a reliable guidance mechanism to reach consistent improvement for the quality of predicted 3D models, particularly in the case of template-based modelling (TBM) targets. Therefore, here we propose to utilize the local quality assessment score produced by ModFOLD6 to guide the MD-based refinement approach to further increase the accuracy of the predicted 3D models. The relative performance of the new local quality assessment guided MD-based refinement protocol and the original MD-based protocol ReFOLD are compared utilizing many different official scoring methods. By using the per-residue accuracy (or local quality) score to guide the refinement process, we are able to prevent the refined models from undesired structural deviations, thereby leading to more consistent improvements. This chapter will include a detailed analysis of the performance of the local quality assessment guided MD-based protocol versus that deployed in the original ReFOLD method.

Pair Potentials as Machine Learning Features

Atom pairwise potential functions make up an essential part of many scoring functions for protein decoy detection. With the development of machine learning (ML) tools, there are multiple ways to combine potential functions to create novel ML models and methods. Potential function parameters can be easily extracted; however, it is usually hard to directly obtain the calculated atom pairwise energies from scoring functions. Amber, as one of the most popular suites of modeling programs, has an extensive history and library of force field potential functions. In this work, we directly used the force field parameters in ff94 and ff14SB from Amber and encoded them to calculate atom pairwise energies for different interactions. Two sets of structures (single amino acid set and a dipeptide set) were used to evaluate the performance of our encoded Amber potentials. From the comparison results between energy terms obtained from our encoding and Amber, we find energy difference within ±0.06 kcal/mol for all tested structures. Previously we have shown that the Random Forest (RF) model can help to emphasize more important atom pairwise interactions and ignore insignificant ones [Pei, J.; Zheng, Z.; Merz, K. M. J. Chem. Inf. Model. 2019, 59, 1919-1929]. Here, as an example of combining ML methods with traditional potential functions, we followed the same work flow to combine the RF models with force field potential functions from Amber. To determine the performance of our RF models with force field potential functions, 224 different protein native-decoy systems were used as our training and testing sets We find that the RF models with ff94 and ff14SB force field parameters outperformed all other scoring functions (RF models with KECSA2, RWplus, DFIRE, dDFIRE, and GOAP) considered in this work for native structure detection, and they performed similarly in detecting the best decoy. Through inclusion of best decoy to decoy comparisons in building our RF models, we were able to generate models that outperformed the score functions tested herein both on accuracy and best decoy detection, again showing the performance and flexibility of our RF models to tackle this problem. Finally, the importance of the RF algorithm and force field parameters were also tested and the comparison results suggest that both the RF algorithm and force field potentials are important with the ML scoring function achieving its best performance only by combining them together. All code and data used in this work are available at https://github.com/JunPei000/FFENCODER_for_Protein_Folding_Pose_Selection.

Ligand-Binding-Site Structure Refinement Using Molecular Dynamics with Restraints Derived from Predicted Binding Site Templates

Accurate modeling of ligand-binding-site structures plays a critical role in structure-based virtual screening. However, the structures of the ligand-binding site in most predicted protein models are generally of low quality and need refinements. In this work, we present a ligand-binding-site structure refinement protocol using molecular dynamics simulation with restraints derived from predicted binding site templates. Our benchmark validation shows great performance for 40 diverse sets of proteins from the Astex list. The ligand-binding sites on modeled protein structures are consistently refined using our method with an average Cα RMSD improvement of 0.90 Å. Comparison of ligand binding modes from ligand docking to initial unrefined and refined structures shows an average of 1.97 Å RMSD improvement in the refined structures. These results demonstrate a promising new method of structure refinement for protein ligand-binding-site structures.

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.

In silico structural elucidation of RNA-dependent RNA polymerase towards the identification of potential Crimean-Congo Hemorrhagic Fever Virus inhibitors

The Crimean-Congo Hemorrhagic Fever virus (CCHFV) is a segmented negative single-stranded RNA virus (-ssRNA) which causes severe hemorrhagic fever in humans with a mortality rate of ~50%. To date, no vaccine has been approved. Treatment is limited to supportive care with few investigational drugs in practice. Previous studies have identified viral RNA dependent RNA Polymerase (RdRp) as a potential drug target due to its significant role in viral replication and transcription. Since no crystal structure is available yet, we report the structural elucidation of CCHFV-RdRp by in-depth homology modeling. Even with low sequence identity, the generated model suggests a similar overall structure as previously reported RdRps. More specifically, the model suggests the presence of structural/functional conserved RdRp motifs for polymerase function, the configuration of uniform spatial arrangement of core RdRp sub-domains, and predicted positively charged entry/exit tunnels, as seen in sNSV polymerases. Extensive pharmacophore modeling based on per-residue energy contribution with investigational drugs allowed the concise mapping of pharmacophoric features and identified potential hits. The combination of pharmacophoric features with interaction energy analysis revealed functionally important residues in the conserved motifs together with in silico predicted common inhibitory binding modes with highly potent reference compounds.

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.

Efficient gaussian density formulation of volume and surface areas of macromolecules on graphical processing units

We present an algorithm to efficiently compute accurate volumes and surface areas of macromolecules on graphical processing unit (GPU) devices using an analytic model which represents atomic volumes by continuous Gaussian densities. The volume of the molecule is expressed by means of the inclusion-exclusion formula, which is based on the summation of overlap integrals among multiple atomic densities. The surface area of the molecule is obtained by differentiation of the molecular volume with respect to atomic radii. The many-body nature of the model makes a port to GPU devices challenging. To our knowledge, this is the first reported full implementation of this model on GPU hardware. To accomplish this, we have used recursive strategies to construct the tree of overlaps and to accumulate volumes and their gradients on the tree data structures so as to minimize memory contention. The algorithm is used in the formulation of a surface area-based non-polar implicit solvent model implemented as an open source plug-in (named GaussVol) for the popular OpenMM library for molecular mechanics modeling. GaussVol is 50 to 100 times faster than our best optimized implementation for the CPUs, achieving speeds in excess of 100 ns/day with 1 fs time-step for protein-sized systems on commodity GPUs. © 2017 Wiley Periodicals, Inc.

FF12MC: A revised AMBER forcefield and new protein simulation protocol

Specialized to simulate proteins in molecular dynamics (MD) simulations with explicit solvation, FF12MC is a combination of a new protein simulation protocol employing uniformly reduced atomic masses by tenfold and a revised AMBER forcefield FF99 with (i) shortened CH bonds, (ii) removal of torsions involving a nonperipheral sp(3) atom, and (iii) reduced 1-4 interaction scaling factors of torsions ϕ and ψ. This article reports that in multiple, distinct, independent, unrestricted, unbiased, isobaric-isothermal, and classical MD simulations FF12MC can (i) simulate the experimentally observed flipping between left- and right-handed configurations for C14-C38 of BPTI in solution, (ii) autonomously fold chignolin, CLN025, and Trp-cage with folding times that agree with the experimental values, (iii) simulate subsequent unfolding and refolding of these miniproteins, and (iv) achieve a robust Z score of 1.33 for refining protein models TMR01, TMR04, and TMR07. By comparison, the latest general-purpose AMBER forcefield FF14SB locks the C14-C38 bond to the right-handed configuration in solution under the same protein simulation conditions. Statistical survival analysis shows that FF12MC folds chignolin and CLN025 in isobaric-isothermal MD simulations 2-4 times faster than FF14SB under the same protein simulation conditions. These results suggest that FF12MC may be used for protein simulations to study kinetics and thermodynamics of miniprotein folding as well as protein structure and dynamics. Proteins 2016; 84:1490-1516. © 2016 The Authors Proteins: Structure, Function, and Bioinformatics Published by Wiley Periodicals, Inc.

Effective protein model structure refinement by loop modeling and overall relaxation

Protein structures predicted by state-of-the-art template-based methods may still have errors when the template proteins are not similar enough to the target protein. Overall target structure may deviate from the template structures owing to differences in sequences. Structural information for some local regions such as loops may not be available when there are sequence insertions or deletions. Those structural aspects that originate from deviations from templates can be dealt with by ab initio structure refinement methods to further improve model accuracy. In the CASP11 refinement experiment, we tested three different refinement methods that utilize overall structure relaxation, loop modeling, and quality assessment of multiple initial structures. From this experiment, we conclude that the overall relaxation method can consistently improve model quality. Loop modeling is the most useful when the initial model structure is high quality, with GDT-HA >60. The method that used multiple initial structures further refined the already refined models; the minor improvements with this method raise the issue of problem with the current energy function. Future research directions are also discussed. Proteins 2016; 84(Suppl 1):293-301. © 2015 Wiley Periodicals, Inc.

Three-dimensional structure and molecular dynamics studies of prorrenin/renin receptor: description of the active site

The recent finding of a specific receptor for prorrenin/renin (PRR) has brought new insights into the physiology of the renin-angiotensin-aldosterone system. No undoubtable role has been described for this receptor so far. Its role seems to be important in chronic illnesses such as hypertension, possibly participating in the cardiovascular remodeling process, and diabetes where participation in inflammation development has been described. It is not possible, however, to explore the PRR function using classical pharmacological approaches due to the lack of specific agonists or antagonists. Two synthetic peptides have been described to accomplish these roles, but no conclusive data have been provided. There are no X-ray crystallography studies available to describe the structure and potential sites for drug development. So, the aim of this work was to model and theoretically describe the PRR. We describe and characterize the whole receptor protein, its spatial conformation and the potential interactions of PRR with the synthetic peptides available, describing the amino acid residues responsible for these interactions. This information provides the basis for directed development of drugs, seeking to agonize or antagonize PRR activity and study its function in health and ill stages.

Significant Refinement of Protein Structure Models Using a Residue-Specific Force Field

An important application of all-atom explicit-solvent molecular dynamics (MD) simulations is the refinement of protein structures from low-resolution experiments or template-based modeling. A critical requirement is that the native structure is stable with the force field. We have applied a recently developed residue-specific force field, RSFF1, to a set of 30 refinement targets from recent CASP experiments. Starting from their experimental structures, 1.0 μs unrestrained simulations at 298 K retain most of the native structures quite well except for a few flexible terminals and long internal loops. Starting from each homology model, a 150 ns MD simulation at 380 K generates the best RMSD improvement of 0.85 Å on average. The structural improvements roughly correlate with the RMSD of the initial homology models, indicating possible consistent structure refinement. Finally, targets TR614 and TR624 have been subjected to long-time replica-exchange MD simulations. Significant structural improvements are generated, with RMSD of 1.91 and 1.36 Å with respect to their crystal structures. Thus, it is possible to achieve realistic refinement of protein structure models to near-experimental accuracy, using accurate force field with sufficient conformational sampling.

Protein NMR structures refined without NOE data

The refinement of low-quality structures is an important challenge in protein structure prediction. Many studies have been conducted on protein structure refinement; the refinement of structures derived from NMR spectroscopy has been especially intensively studied. In this study, we generated flat-bottom distance potential instead of NOE data because NOE data have ambiguity and uncertainty. The potential was derived from distance information from given structures and prevented structural dislocation during the refinement process. A simulated annealing protocol was used to minimize the potential energy of the structure. The protocol was tested on 134 NMR structures in the Protein Data Bank (PDB) that also have X-ray structures. Among them, 50 structures were used as a training set to find the optimal "width" parameter in the flat-bottom distance potential functions. In the validation set (the other 84 structures), most of the 12 quality assessment scores of the refined structures were significantly improved (total score increased from 1.215 to 2.044). Moreover, the secondary structure similarity of the refined structure was improved over that of the original structure. Finally, we demonstrate that the combination of two energy potentials, statistical torsion angle potential (STAP) and the flat-bottom distance potential, can drive the refinement of NMR structures.

Building Force Fields: An Automatic, Systematic, and Reproducible Approach

The development of accurate molecular mechanics force fields is a significant challenge that must be addressed for the continued success of molecular simulation. We developed the ForceBalance method to automatically derive accurate force field parameters using flexible combinations of experimental and theoretical reference data. The method is demonstrated in the parametrization of two rigid water models, yielding new parameter sets (TIP3P-FB and TIP4P-FB) that accurately describe many physical properties of water.

Physics-based protein structure refinement through multiple molecular dynamics trajectories and structure averaging

We used molecular dynamics (MD) simulations for structure refinement of Critical Assessment of Techniques for Protein Structure Prediction 10 (CASP10) targets. Refinement was achieved by selecting structures from the MD-based ensembles followed by structural averaging. The overall performance of this method in CASP10 is described, and specific aspects are analyzed in detail to provide insight into key components. In particular, the use of different restraint types, sampling from multiple short simulations versus a single long simulation, the success of a quality assessment criterion, the application of scoring versus averaging, and the impact of a final refinement step are discussed in detail.

In Silico Molecular Characterization of Cysteine Protease YopT from Yersinia pestis by Homology Modeling and Binding Site Identification

Plague is a major health concern and Yersinia pestis plays the central causal role in this disease. Yersinia pestis has developed resistance against the commonly available drugs. So, it is now a key concern to find a new drug target. Cysteine protease YopT enzyme is an important factor used by Yersinia pestis for pathogenesis in its host and it has the anti-phagocytic function of removal of C-termini lipid modification. The 3D structure of cysteine protease YopT of Yersinia pestis was determined by means of homology modeling through multiple alignments followed by intensive optimization and validation. The modeling was done by Phyre 2 and refined by ModRefiner. The obtained model was verified with structure validation programs such as PROCHECK, verify 3D and ERRAT for reliability. Interacting partners and active sites were also determined. PROCHECK analysis showed that 93% of the residues are in the most favored region, 5.9% are in the additional allowed region and 1.1% are in the generously allowed region of the Ramachandran plot. The verify 3D value of 0.78 indicates that the environmental profile of the model is good. SOPMA is employed for calculation of the secondary structural features of cysteine protease YopT. Active site determination through CASTp proposes that this protein can be utilized as a potential drug target. However, these findings should further be confirmed by wet lab studies for a targeted therapeutic agent design against Yersinia pestis.

ITScorePro: an efficient scoring program for evaluating the energy scores of protein structures for structure prediction

One important component in protein structure prediction is to evaluate the free energy of a given conformation. Given the enormous number of possible conformations for a sequence, it is extremely challenging to quickly and accurately score the energies of these conformations and predict a reasonable structure within a practical computational time. Here, we describe an efficient program for energy evaluation, referred to as ITScorePro (Copyright © 2012). The energy scoring function in the ITScorePro program is based on the distance-dependent, pairwise atomic potentials for protein structure prediction that we recently derived by using statistical mechanics principles (Huang and Zou, Proteins 79:2648-2661, 2011). ITScorePro is a stand-alone program and can also be easily implemented in other software suites for protein structure prediction.

Forcefield_PTM: Ab Initio Charge and AMBER Forcefield Parameters for Frequently Occurring Post-Translational Modifications

In this work, we introduce Forcefield_PTM, a set of AMBER forcefield parameters consistent with ff03 for 32 common post-translational modifications. Partial charges were calculated through ab initio calculations and a two-stage RESP-fitting procedure in an ether-like implicit solvent environment. The charges were found to be generally consistent with others previously reported for phosphorylated amino acids, and trimethyllysine, using different parameterization methods. Pairs of modified and their corresponding unmodified structures were curated from the PDB for both single and multiple modifications. Background structural similarity was assessed in the context of secondary and tertiary structures from the global dataset. Next, the charges derived for Forcefield_PTM were tested on a macroscopic scale using unrestrained all-atom Langevin molecular dynamics simulations in AMBER for 34 (17 pairs of modified/unmodified) systems in implicit solvent. Assessment was performed in the context of secondary structure preservation, stability in energies, and correlations between the modified and unmodified structure trajectories on the aggregate. As an illustration of their utility, the parameters were used to compare the structural stability of the phosphorylated and dephosphorylated forms of OdhI. Microscopic comparisons between quantum and AMBER single point energies along key χ torsions on several PTMs were performed and corrections to improve their agreement in terms of mean squared errors and squared correlation coefficients were parameterized. This forcefield for post-translational modifications in condensed-phase simulations can be applied to a number of biologically relevant and timely applications including protein structure prediction, protein and peptide design, docking, and to study the effect of PTMs on folding and dynamics. We make the derived parameters and an associated interactive webtool capable of performing post-translational modifications on proteins using Forcefield_PTM available at http://selene.princeton.edu/FFPTM.

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.

i3Drefine software for protein 3D structure refinement and its assessment in CASP10

Protein structure refinement refers to the process of improving the qualities of protein structures during structure modeling processes to bring them closer to their native states. Structure refinement has been drawing increasing attention in the community-wide Critical Assessment of techniques for Protein Structure prediction (CASP) experiments since its addition in 8^th CASP experiment. During the 9^th and recently concluded 10^th CASP experiments, a consistent growth in number of refinement targets and participating groups has been witnessed. Yet, protein structure refinement still remains a largely unsolved problem with majority of participating groups in CASP refinement category failed to consistently improve the quality of structures issued for refinement. In order to alleviate this need, we developed a completely automated and computationally efficient protein 3D structure refinement method, i3Drefine, based on an iterative and highly convergent energy minimization algorithm with a powerful all-atom composite physics and knowledge-based force fields and hydrogen bonding (HB) network optimization technique. In the recent community-wide blind experiment, CASP10, i3Drefine (as ‘MULTICOM-CONSTRUCT’) was ranked as the best method in the server section as per the official assessment of CASP10 experiment. Here we provide the community with free access to i3Drefine software and systematically analyse the performance of i3Drefine in strict blind mode on the refinement targets issued in CASP10 refinement category and compare with other state-of-the-art refinement methods participating in CASP10. Our analysis demonstrates that i3Drefine is only fully-automated server participating in CASP10 exhibiting consistent improvement over the initial structures in both global and local structural quality metrics. Executable version of i3Drefine is freely available at http://protein.rnet.missouri.edu/i3drefine/.

Protein Structure Refinement through Structure Selection and Averaging from Molecular Dynamics Ensembles

A molecular dynamics (MD) simulation based protocol for structure refinement of template-based model predictions is described. The protocol involves the application of restraints, ensemble averaging of selected subsets, interpolation between initial and refined structures, and assessment of refinement success. It is found that sub-microsecond MD-based sampling when combined with ensemble averaging can produce moderate but consistent refinement for most systems in the CASP targets considered here.

3Drefine: consistent protein structure refinement by optimizing hydrogen bonding network and atomic-level energy minimization

One of the major limitations of computational protein structure prediction is the deviation of predicted models from their experimentally derived true, native structures. The limitations often hinder the possibility of applying computational protein structure prediction methods in biochemical assignment and drug design that are very sensitive to structural details. Refinement of these low-resolution predicted models to high-resolution structures close to the native state, however, has proven to be extremely challenging. Thus, protein structure refinement remains a largely unsolved problem. Critical assessment of techniques for protein structure prediction (CASP) specifically indicated that most predictors participating in the refinement category still did not consistently improve model quality. Here, we propose a two-step refinement protocol, called 3Drefine, to consistently bring the initial model closer to the native structure. The first step is based on optimization of hydrogen bonding (HB) network and the second step applies atomic-level energy minimization on the optimized model using a composite physics and knowledge-based force fields. The approach has been evaluated on the CASP benchmark data and it exhibits consistent improvement over the initial structure in both global and local structural quality measures. 3Drefine method is also computationally inexpensive, consuming only few minutes of CPU time to refine a protein of typical length (300 residues). 3Drefine web server is freely available at http://sysbio.rnet.missouri.edu/3Drefine/.

Refinement of protein structure homology models via long, all-atom molecular dynamics simulations

Accurate computational prediction of protein structure represents a longstanding challenge in molecular biology and structure-based drug design. Although homology modeling techniques are widely used to produce low-resolution models, refining these models to high resolution has proven difficult. With long enough simulations and sufficiently accurate force fields, molecular dynamics (MD) simulations should in principle allow such refinement, but efforts to refine homology models using MD have for the most part yielded disappointing results. It has thus far been unclear whether MD-based refinement is limited primarily by accessible simulation timescales, force field accuracy, or both. Here, we examine MD as a technique for homology model refinement using all-atom simulations, each at least 100 μs long-more than 100 times longer than previous refinement simulations-and a physics-based force field that was recently shown to successfully fold a structurally diverse set of fast-folding proteins. In MD simulations of 24 proteins chosen from the refinement category of recent Critical Assessment of Structure Prediction (CASP) experiments, we find that in most cases, simulations initiated from homology models drift away from the native structure. Comparison with simulations initiated from the native structure suggests that force field accuracy is the primary factor limiting MD-based refinement. This problem can be mitigated to some extent by restricting sampling to the neighborhood of the initial model, leading to structural improvement that, while limited, is roughly comparable to the leading alternative methods.

Structure refinement of protein low resolution models using the GNEIMO constrained dynamics method

The challenge in protein structure prediction using homology modeling is the lack of reliable methods to refine the low resolution homology models. Unconstrained all-atom molecular dynamics (MD) does not serve well for structure refinement due to its limited conformational search. We have developed and tested the constrained MD method, based on the generalized Newton-Euler inverse mass operator (GNEIMO) algorithm for protein structure refinement. In this method, the high-frequency degrees of freedom are replaced with hard holonomic constraints and a protein is modeled as a collection of rigid body clusters connected by flexible torsional hinges. This allows larger integration time steps and enhances the conformational search space. In this work, we have demonstrated the use of torsional GNEIMO method without using any experimental data as constraints, for protein structure refinement starting from low-resolution decoy sets derived from homology methods. In the eight proteins with three decoys for each, we observed an improvement of ~2 Å in the rmsd in coordinates to the known experimental structures of these proteins. The GNEIMO trajectories also showed enrichment in the population density of native-like conformations. In addition, we demonstrated structural refinement using a "freeze and thaw" clustering scheme with the GNEIMO framework as a viable tool for enhancing localized conformational search. We have derived a robust protocol based on the GNEIMO replica exchange method for protein structure refinement that can be readily extended to other proteins and possibly applicable for high throughput protein structure refinement.

GOAP: a generalized orientation-dependent, all-atom statistical potential for protein structure prediction

An accurate scoring function is a key component for successful protein structure prediction. To address this important unsolved problem, we develop a generalized orientation and distance-dependent all-atom statistical potential. The new statistical potential, generalized orientation-dependent all-atom potential (GOAP), depends on the relative orientation of the planes associated with each heavy atom in interacting pairs. GOAP is a generalization of previous orientation-dependent potentials that consider only representative atoms or blocks of side-chain or polar atoms. GOAP is decomposed into distance- and angle-dependent contributions. The DFIRE distance-scaled finite ideal gas reference state is employed for the distance-dependent component of GOAP. GOAP was tested on 11 commonly used decoy sets containing 278 targets, and recognized 226 native structures as best from the decoys, whereas DFIRE recognized 127 targets. The major improvement comes from decoy sets that have homology-modeled structures that are close to native (all within ∼4.0 Å) or from the ROSETTA ab initio decoy set. For these two kinds of decoys, orientation-independent DFIRE or only side-chain orientation-dependent RWplus performed poorly. Although the OPUS-PSP block-based orientation-dependent, side-chain atom contact potential performs much better (recognizing 196 targets) than DFIRE, RWplus, and dDFIRE, it is still ∼15% worse than GOAP. Thus, GOAP is a promising advance in knowledge-based, all-atom statistical potentials. GOAP is available for download at http://cssb.biology.gatech.edu/GOAP.

Force fields for homology modeling

Accurate all-atom energy functions are crucial for successful high-resolution protein structure prediction. In this chapter, we review both physics-based force fields and knowledge-based potentials used in protein modeling. Because it is important to calculate the energy as accurately as possible given the limitations imposed by sampling convergence, different components of the energy, and force fields representing them to varying degrees of detail and complexity are discussed. Force fields using Cartesian as well as torsion angle representations of protein geometry are covered. Since solvent is important for protein energetics, different aqueous and membrane solvation models for protein simulations are also described. Finally, we summarize recent progress in protein structure refinement using new force fields.

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.

Assessment of protein structure refinement in CASP9

We assess performance in the structure refinement category in CASP9. Two years after CASP8, the performance of the best groups has not improved. There are few groups that improve any of our assessment scores with statistical significance. Some predictors, however, are able to consistently improve the physicality of the models. Although we cannot identify any clear bottleneck in improving refinement, several points arise: (1) The refinement portion of CASP has too few targets to make many statistically meaningful conclusions. (2) Predictors are usually very conservative, limiting the possibility of large improvements in models. (3) No group is actually able to correctly rank their five submissions-indicating that potentially better models may be discarded. (4) Different sampling strategies work better for different refinement problems; there is no single strategy that works on all targets. In general, conservative strategies do better, while the greatest improvements come from more adventurous sampling-at the cost of consistency. Comparison with experimental data reveals aspects not captured by comparison to a single structure. In particular, we show that improvement in backbone geometry does not always mean better agreement with experimental data. Finally, we demonstrate that even given the current challenges facing refinement, the refined models are useful for solving the crystallographic phase problem through molecular replacement. Proteins 2011;. © 2011 Wiley-Liss, Inc.

Comparison between self-guided Langevin dynamics and molecular dynamics simulations for structure refinement of protein loop conformations

This article presents a comparative analysis of two replica-exchange simulation methods for the structure refinement of protein loop conformations, starting from low-resolution predictions. The methods are self-guided Langevin dynamics (SGLD) and molecular dynamics (MD) with a Nosé-Hoover thermostat. We investigated a small dataset of 8- and 12-residue loops, with the shorter loops placed initially from a coarse-grained lattice model and the longer loops from an enumeration assembly method (the Loopy program). The CHARMM22 + CMAP force field with a generalized Born implicit solvent model (molecular-surface parameterized GBSW2) was used to explore conformational space. We also assessed two empirical scoring methods to detect nativelike conformations from decoys: the all-atom distance-scaled ideal-gas reference state (DFIRE-AA) statistical potential and the Rosetta energy function. Among the eight-residue loop targets, SGLD out performed MD in all cases, with a median of 0.48 Å reduction in global root-mean-square deviation (RMSD) of the loop backbone coordinates from the native structure. Among the more challenging 12-residue loop targets, SGLD improved the prediction accuracy over MD by a median of 1.31 Å, representing a substantial improvement. The overall median RMSD for SGLD simulations of 12-residue loops was 0.91 Å, yielding refinement of a median 2.70 Å from initial loop placement. Results from DFIRE-AA and the Rosetta model applied to rescoring conformations failed to improve the overall detection calculated from the CHARMM force field. We illustrate the advantage of SGLD over the MD simulation model by presenting potential-energy landscapes for several loop predictions. Our results demonstrate that SGLD significantly outperforms traditional MD in the generation and populating of nativelike loop conformations and that the CHARMM force field performs comparably to other empirical force fields in identifying these conformations from the resulting ensembles.

Optimization of Monte Carlo trial moves for protein simulations

Closed rigid-body rotations of residue segments under bond-angle restraints are simple and effective Monte Carlo moves for searching the conformational space of proteins. The efficiency of these moves is examined here as a function of the number of moving residues and the magnitude of their displacement. It is found that the efficiency of folding and equilibrium simulations can be significantly improved by tailoring the distribution of the number of moving residues to the simulation temperature. In general, simulations exploring compact conformations are more efficient when the average number of moving residues is smaller. It is also demonstrated that the moves do not require additional restrictions on the magnitude of the rotation displacements and perform much better than other rotation moves that do not restrict the bond angles a priori. As an example, these results are applied to the replica exchange method. By assigning distributions that generate a smaller number of moving residues to lower temperature replicas, the simulation times are decreased as long as the higher temperature replicas are effective.

Trends in template/fragment-free protein structure prediction

Predicting the structure of a protein from its amino acid sequence is a long-standing unsolved problem in computational biology. Its solution would be of both fundamental and practical importance as the gap between the number of known sequences and the number of experimentally solved structures widens rapidly. Currently, the most successful approaches are based on fragment/template reassembly. Lacking progress in template-free structure prediction calls for novel ideas and approaches. This article reviews trends in the development of physical and specific knowledge-based energy functions as well as sampling techniques for fragment-free structure prediction. Recent physical- and knowledge-based studies demonstrated that it is possible to sample and predict highly accurate protein structures without borrowing native fragments from known protein structures. These emerging approaches with fully flexible sampling have the potential to move the field forward.

Symmetry-restrained molecular dynamics simulations improve homology models of potassium channels

Most crystallized homo-oligomeric ion channels are highly symmetric, which dramatically decreases conformational space and facilitates building homology models (HMs). However, in molecular dynamics (MD) simulations channels deviate from ideal symmetry and accumulate thermal defects, which complicate the refinement of HMs using MD. In this work we evaluate the ability of symmetry constrained MD simulations to improve HMs accuracy, using an approach conceptually similar to Critical Assessment of techniques for protein Structure Prediction (CASP) competition: build HMs of channels with known structure and evaluate the efficiency of proposed methods in improving HMs accuracy (measured as deviation from experimental structure). Results indicate that unrestrained MD does not improve the accuracy of HMs, instantaneous symmetrization improves accuracy but not stability of HMs during subsequent unrestrained MD, while gradually imposing symmetry constraints improves both accuracy (by 5-50%) and stability of HMs. Moreover, accuracy and stability are strongly correlated, making stability a reliable criterion in predicting the accuracy of new HMs. Proteins 2010. (c) 2009 Wiley-Liss, Inc.

Prediction of 3D metal binding sites from translated gene sequences based on remote-homology templates

Database-scale analysis was performed to determine whether structural models, based on remote homologues, are effective in predicting 3D transition metal binding sites in proteins directly from translated gene sequences. The extent by which side chain modeling alone reduces sensitivity and selectivity is shown to be <10%. Surprisingly, selectivity was not dependent on the level of sequence homology between template and target, or on the presence of a metal ion in the structural template. Applying a modification of the CHED algorithm (Babor et al., Proteins 2008;70:208-217) and machine learning filters, a selectivity of approximately 90% was achieved for protein sequences using unrelated structural templates over a sequence identity range of 18-100%. Below approximately 18% identity, the number of analyzable target-template pairs and predictability of metal binding sites falls off sharply. A full third of structural templates were found to have target partners only in the remote homology range of 18-30%. In this range, nonmetal-binding templates are calculated to be the majority and serve to predict with 50% sensitivity at the geometric level. Overall, sensitivity at the geometric level for targets having templates in the 18-30% sequence identity range is 73%, with an average of one false positive site per true site. Protein sequences described as "unknown" in the UniProt database and composed largely of unidentified genome project sequences were studied and metal binding sites predicted. A web server for prediction of metal binding sites from protein sequence is provided.

Assessment of the protein-structure refinement category in CASP8

Here, we summarize the assessment of protein structure refinement in CASP8. Twenty-four groups refined a total of 12 target proteins. Averaging over all groups and all proteins, there was no net improvement over the original starting models. However, there are now some individual research groups who consistently do improve protein structures relative to a starting starting model. We compare various measures of quality assessment, including (i) standard backbone-based methods, (ii) new methods from the Richardson group, and (iii) ensemble-based methods for comparing experimental structures, such as NMR NOE violations and the suitability of the predicted models to serve as templates for molecular replacement. On the whole, there is a general correlation among various measures. However, there are interesting differences. Sometimes a structure that is in better agreement with the experimental data is judged to be slightly worse by GDT-TS. This suggests that for comparing protein structures that are already quite close to the native, it may be preferable to use ensemble-based experimentally derived measures of quality, in addition to single-structure-based methods such as GDT-TS.

Discriminating the native structure from decoys using scoring functions based on the residue packing in globular proteins

BACKGROUND

Setting the rules for the identification of a stable conformation of a protein is of utmost importance for the efficient generation of structures in computer simulation. For structure prediction, a considerable number of possible models are generated from which the best model has to be selected.

RESULTS

Two scoring functions, Rs and Rp, based on the consideration of packing of residues, which indicate if the conformation of an amino acid sequence is native-like, are presented. These are defined using the solvent accessible surface area (ASA) and the partner number (PN) (other residues that are within 4.5 A) of a particular residue. The two functions evaluate the deviation from the average packing properties (ASA or PN) of all residues in a polypeptide chain corresponding to a model of its three-dimensional structure. While simple in concept and computationally less intensive, both the functions are at least as efficient as any other energy functions in discriminating the native structure from decoys in a large number of standard decoy sets, as well as on models submitted for the targets of CASP7. Rs appears to be slightly more effective than Rp, as determined by the number of times the native structure possesses the minimum value for the function and its separation from the average value for the decoys.

CONCLUSION

Two parameters, Rs and Rp, are discussed that can very efficiently recognize the native fold for a sequence from an ensemble of decoy structures. Unlike many other algorithms that rely on the use of composite scoring function, these are based on a single parameter, viz., the accessible surface area (or the number of residues in contact), but still able to capture the essential attribute of the native fold.

Splitting statistical potentials into meaningful scoring functions: testing the prediction of near-native structures from decoy conformations

Background

Recent advances on high-throughput technologies have produced a vast amount of protein sequences, while the number of high-resolution structures has seen a limited increase. This has impelled the production of many strategies to built protein structures from its sequence, generating a considerable amount of alternative models. The selection of the closest model to the native conformation has thus become crucial for structure prediction. Several methods have been developed to score protein models by energies, knowledge-based potentials and combination of both.

Results

Here, we present and demonstrate a theory to split the knowledge-based potentials in scoring terms biologically meaningful and to combine them in new scores to predict near-native structures. Our strategy allows circumventing the problem of defining the reference state. In this approach we give the proof for a simple and linear application that can be further improved by optimizing the combination of Zscores. Using the simplest composite score () we obtained predictions similar to state-of-the-art methods. Besides, our approach has the advantage of identifying the most relevant terms involved in the stability of the protein structure. Finally, we also use the composite Zscores to assess the conformation of models and to detect local errors.

Conclusion

We have introduced a method to split knowledge-based potentials and to solve the problem of defining a reference state. The new scores have detected near-native structures as accurately as state-of-art methods and have been successful to identify wrongly modeled regions of many near-native conformations.

A coarse-grained potential for fold recognition and molecular dynamics simulations of proteins

A coarse-grained potential for protein simulations and fold ranking is presented. The potential is based on a two-point model of individual amino acids and a specific implementation of hydrogen bonding. Parameters are determined for distance dependent pair interactions, pseudo bonds, angles, and torsions. A scaling factor for a hydrogen bonding term is also determined. Iterative sampling for 4867 proteins reproduces distributions of internal coordinates and distances observed in the Protein Data Bank. The adjustment of the potential and resampling are in the spirit of the generalized ensemble approach. No native structure information (e.g., secondary structure) is used in the calculation of the potential or in the simulation of a particular protein. The potential is subject to two tests as follows: (i) simulations of 956 globular proteins in the neighborhood of their native folds (these proteins were not used in the training set) and (ii) discrimination between native and decoy structures for 2470 proteins with 305,000 decoys and the "Decoys 'R' Us" dataset. In the first test, 58% of tested proteins stay within 5 A from the native fold in Molecular Dynamics simulations of more than 20 nanoseconds using the new potential. The potential is also useful in differentiating between correct and approximate folds providing significant signal for structure prediction algorithms. Sampling with the potential consistently regenerates the distribution of distances and internal coordinates it learned. Nevertheless, during Molecular Dynamics simulations structures are found that reproduce the learned distributions but are far from the native fold.

A novel method for predicting and using distance constraints of high accuracy for refining protein structure prediction

The principal bottleneck in protein structure prediction is the refinement of models from lower accuracies to the resolution observed by experiment. We developed a novel constraints-based refinement method that identifies a high number of accurate input constraints from initial models and rebuilds them using restrained torsion angle dynamics (rTAD). We previously created a Bayesian statistics-based residue-specific all-atom probability discriminatory function (RAPDF) to discriminate native-like models by measuring the probability of accuracy for atom type distances within a given model. Here, we exploit RAPDF to score (i.e., filter) constraints from initial predictions that may or may not be close to a native-like state, obtain consensus of top scoring constraints amongst five initial models, and compile sets with no redundant residue pair constraints. We find that this method consistently produces a large and highly accurate set of distance constraints from which to build refinement models. We further optimize the balance between accuracy and coverage of constraints by producing multiple structure sets using different constraint distance cutoffs, and note that the cutoff governs spatially near versus distant effects in model generation. This complete procedure of deriving distance constraints for rTAD simulations improves the quality of initial predictions significantly in all cases evaluated by us. Our procedure represents a significant step in solving the protein structure prediction and refinement problem, by enabling the use of consensus constraints, RAPDF, and rTAD for protein structure modeling and refinement.

Force field bias in protein folding simulations

Long timescale (>1 micros) molecular dynamics simulations of protein folding offer a powerful tool for understanding the atomic-scale interactions that determine a protein's folding pathway and stabilize its native state. Unfortunately, when the simulated protein fails to fold, it is often unclear whether the failure is due to a deficiency in the underlying force fields or simply a lack of sufficient simulation time. We examine one such case, the human Pin1 WW domain, using the recently developed deactivated morphing method to calculate free energy differences between misfolded and folded states. We find that the force field we used favors the misfolded states, explaining the failure of the folding simulations. Possible further applications of deactivated morphing and implications for force field development are discussed.

Protein structure prediction: when is it useful?

Computationally predicted three-dimensional structure of protein molecules has demonstrated the usefulness in many areas of biomedicine, ranging from approximate family assignments to precise drug screening. For nearly 40 years, however, the accuracy of the predicted models has been dictated by the availability of close structural templates. Progress has recently been achieved in refining low-resolution models closer to the native ones; this has been made possible by combining knowledge-based information from multiple sources of structural templates as well as by improving the energy funnel of physics-based force fields. Unfortunately, there has been no essential progress in the development of techniques for detecting remotely homologous templates and for predicting novel protein structures.

Generalized ensemble methods for de novo structure prediction

Current methods for predicting protein structure depend on two interrelated components: (i) an energy function that should have a low value near the correct structure and (ii) a method for searching through different conformations of the polypeptide chain. Identification of the most efficient search methods is essential if we are to be able to apply such methods broadly and with confidence. In addition, efficient search methods provide a rigorous test of existing energy functions, which are generally knowledge-based and contain different terms added together with arbitrary weights. Here, we test different search methods with one of the most accurate and predictive energy functions, namely Rosetta the knowledge-based force-field from Baker's group [Simons K, Kooperberg C, Huang E, Baker D (1997) J Mol Biol 268:209-225]. We use an implementation of a generalized ensemble search method to scale relevant parts of the energy function. This method, known as Hamiltonian Replica Exchange Monte Carlo, outperforms the original Monte Carlo Simulated Annealing used in the Rosetta package in terms of sampling low-energy states. It also outperforms another widely used generalized ensemble search method known as Temperature Replica Exchange Monte Carlo. Our results reveal clear deficiencies in the low-resolution Rosetta energy function in that the lowest energy structures are not necessarily the most native-like. By using a set of nonnative low-energy structures found by our extensive sampling, we discovered that the long-range and short-range backbone hydrogen-bonding energy terms of the Rosetta energy discriminate between the nonnative and native-like structures significantly better than the low-resolution score used in Rosetta.