Folding simulations of Trp‐cage mini protein in explicit solvent using biasing potential replica‐exchange molecular dynamics simulations

Replica exchange molecular dynamics (RexMD) simulations are frequently used for studying structure formation and dynamics of peptides and proteins. A significant drawback of standard temperature RexMD is, however, the rapid increase of the replica number with increasing system size to cover a desired temperature range. A recently developed Hamiltonian RexMD method has been used to study folding of the Trp‐cage protein. It employs a biasing potential that lowers the backbone dihedral barriers and promotes peptide backbone transitions along the replica coordinate. In two independent applications of the biasing potential RexMD method including explicit solvent and starting from a completely unfolded structure the formation of near‐native conformations was observed after 30–40 ns simulation time. The conformation representing the most populated cluster at the final simulation stage had a backbone root mean square deviation of ～1.3 Å from the experimental structure. This was achieved with a very modest number of five replicas making it well suited for peptide and protein folding and refinement studies including explicit solvent. In contrast, during five independent continuous 70 ns molecular dynamics simulations formation of collapsed states but no near native structure formation was observed. The simulations predict a largely collapsed state with a significant helical propensity for the helical domain of the Trp‐cage protein already in the unfolded state. Hydrogen bonded bridging water molecules were identified that could play an active role by stabilizing the arrangement of the helical domain with respect to the rest of the chain already in intermediate states of the protein. Proteins 2009. © 2008 Wiley‐Liss, Inc.     

Driven to near-experimental accuracy by refinement via molecular dynamics simulations

Protein model refinement has been an essential part of successful protein structure prediction. Molecular dynamics simulation-based refinement methods have shown consistent improvement of protein models. There had been progress in the extent of refinement for a few years since the idea of ensemble averaging of sampled conformations emerged. There was little progress in CASP12 because conformational sampling was not sufficiently diverse due to harmonic restraints. During CASP13, a new refinement method was tested that achieved significant improvements over CASP12. The new method intended to address previous bottlenecks in the refinement problem by introducing new features. Flat-bottom harmonic restraints replaced harmonic restraints, sampling was performed iteratively, and a new scoring function and selection criteria were used. The new protocol expanded conformational sampling at reduced computational costs. In addition to overall improvements, some models were refined significantly to near-experimental accuracy.     

Mimicking the action of folding chaperones in molecular dynamics simulations: Application to the refinement of homology-based protein structures

A novel method for the refinement of misfolded protein structures is proposed in which the properties of the solvent environment are oscillated in order to mimic some aspects of the role of molecular chaperones play in protein folding in vivo. Specifically, the hydrophobicity of the solvent is cycled by repetitively altering the partial charges on solvent molecules (water) during a molecular dynamics simulation. During periods when the hydrophobicity of the solvent is increased, intramolecular hydrogen bonding and secondary structure formation are promoted. During periods of increased solvent polarity, poorly packed regions of secondary structures are destabilized, promoting structural rearrangement. By cycling between these two extremes, the aim is to minimize the formation of long-lived intermediates. The approach has been applied to the refinement of structural models of three proteins generated by using the ROSETTA procedure for ab initio structure prediction. A significant improvement in the deviation of the model structures from the corresponding experimental structures was observed. Although preliminary, the results indicate computationally mimicking some functions of molecular chaperones in molecular dynamics simulations can promote the correct formation of secondary structure and thus be of general use in protein folding simulations and in the refinement of structural models of small- to medium-size proteins.     

Enhanced sampling of peptide and protein conformations using replica exchange simulations with a peptide backbone biasing-potential

During replica exchange molecular dynamics (RexMD) simulations, several replicas of a system are simulated at different temperatures in parallel allowing for exchange between replicas at frequent intervals. This technique allows significantly improved sampling of conformational space and is increasingly being used for structure prediction of peptides and proteins. A drawback of the standard temperature RexMD is the rapid increase of the replica number with increasing system size to cover a desired temperature range. In an effort to limit the number of replicas, a new Hamiltonian-RexMD method has been developed that is specifically designed to enhance the sampling of peptide and protein conformations by applying various levels of a backbone biasing potential for each replica run. The biasing potential lowers the barrier for backbone dihedral transitions and promotes enhanced peptide backbone transitions along the replica coordinate. The application on several peptide cases including in all cases explicit solvent indicates significantly improved conformational sampling when compared with standard MD simulations. This was achieved with a very modest number of 5-7 replicas for each simulation system making it ideally suited for peptide and protein folding simulations as well as refinement of protein model structures in the presence of explicit solvent.     

Structure refinement of protein model decoys requires accurate side‐chain placement

In this study, the application of temperature‐based replica‐exchange (T‐ReX) simulations for structure refinement of decoys taken from the I‐TASSER dataset was examined. A set of eight nonredundant proteins was investigated using self‐guided Langevin dynamics (SGLD) with a generalized Born implicit solvent model to sample conformational space. For two of the protein test cases, a comparison of the SGLD/T‐ReX method with that of a hybrid explicit/implicit solvent molecular dynamics T‐ReX simulation model is provided. Additionally, the effect of side‐chain placement among the starting decoy structures, using alternative rotamer conformations taken from the SCWRL4 modeling program, was investigated. The simulation results showed that, despite having near‐native backbone conformations among the starting decoys, the determinant of their refinement is side‐chain packing to a level that satisfies a minimum threshold of native contacts to allow efficient excursions toward the downhill refinement regime on the energy landscape. By repacking using SCWRL4 and by applying the RWplus statistical potential for structure identification, the SGLD/T‐ReX simulations achieved refinement to an average of 38% increase in the number of native contacts relative to the original I‐TASSER decoy sets and a 25% reduction in values of C_α root‐mean‐square deviation. The hybrid model succeeded in obtaining a sharper funnel to low‐energy states for a modeled target than the implicit solvent SGLD model; yet, structure identification remained roughly the same. Without meeting a threshold of near‐native packing of side chains, the T‐ReX simulations degrade the accuracy of the decoys, and subsequently, refinement becomes tantamount to the protein folding problem. Proteins 2013. 2012 Published by Wiley Periodicals, Inc.     

Structure refinement of membrane proteins via molecular dynamics simulations

A refinement protocol based on physics‐based techniques established for water soluble proteins is tested for membrane protein structures. Initial structures were generated by homology modeling and sampled via molecular dynamics simulations in explicit lipid bilayer and aqueous solvent systems. Snapshots from the simulations were selected based on scoring with either knowledge‐based or implicit membrane‐based scoring functions and averaged to obtain refined models. The protocol resulted in consistent and significant refinement of the membrane protein structures similar to the performance of refinement methods for soluble proteins. Refinement success was similar between sampling in the presence of lipid bilayers and aqueous solvent but the presence of lipid bilayers may benefit the improvement of lipid‐facing residues. Scoring with knowledge‐based functions (DFIRE and RWplus) was found to be as good as scoring using implicit membrane‐based scoring functions suggesting that differences in internal packing is more important than orientations relative to the membrane during the refinement of membrane protein homology models.     

Princeton_TIGRESS: Protein geometry refinement using simulations and support vector machines

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

Mimicking the action of GroEL in molecular dynamics simulations: application to the refinement of protein structures

Bacterial chaperonin, GroEL, together with its co-chaperonin, GroES, facilitates the folding of a variety of polypeptides. Experiments suggest that GroEL stimulates protein folding by multiple cycles of binding and release. Misfolded proteins first bind to an exposed hydrophobic surface on GroEL. GroES then encapsulates the substrate and triggers its release into the central cavity of the GroEL/ES complex for folding. In this work, we investigate the possibility to facilitate protein folding in molecular dynamics simulations by mimicking the effects of GroEL/ES namely, repeated binding and release, together with spatial confinement. During the binding stage, the (metastable) partially folded proteins are allowed to attach spontaneously to a hydrophobic surface within the simulation box. This destabilizes the structures, which are then transferred into a spatially confined cavity for folding. The approach has been tested by attempting to refine protein structural models generated using the ROSETTA procedure for ab initio structure prediction. Dramatic improvements in regard to the deviation of protein models from the corresponding experimental structures were observed. The results suggest that the primary effects of the GroEL/ES system can be mimicked in a simple coarse-grained manner and be used to facilitate protein folding in molecular dynamics simulations. Furthermore, the results support the assumption that the spatial confinement in GroEL/ES assists the folding of encapsulated proteins.     

Prediction of structures of zinc‐binding proteins through explicit modeling of metal coordination geometry

Metal ions play an essential role in stabilizing protein structures and contributing to protein function. Ions such as zinc have well‐defined coordination geometries, but it has not been easy to take advantage of this knowledge in protein structure prediction efforts. Here, we present a computational method to predict structures of zinc‐binding proteins given knowledge of the positions of zinc‐coordinating residues in the amino acid sequence. The method takes advantage of the “atom‐tree” representation of molecular systems and modular architecture of the Rosetta3 software suite to incorporate explicit metal ion coordination geometry into previously developed de novo prediction and loop modeling protocols. Zinc cofactors are tethered to their interacting residues based on coordination geometries observed in natural zinc‐binding proteins. The incorporation of explicit zinc atoms and their coordination geometry in both de novo structure prediction and loop modeling significantly improves sampling near the native conformation. The method can be readily extended to predict protein structures bound to other metal and/or small chemical cofactors with well‐defined coordination or ligation geometry.     

Fast de novo discovery of low‐energy protein loop conformations

In the prediction of protein structure from amino acid sequence, loops are challenging regions for computational methods. Since loops are often located on the protein surface, they can have significant roles in determining protein functions and binding properties. Loop prediction without the aid of a structural template requires extensive conformational sampling and energy minimization, which are computationally difficult. In this article we present a new de novo loop sampling method, the Parallely filtered Energy Targeted All‐atom Loop Sampler (PETALS) to rapidly locate low energy conformations. PETALS explores both backbone and side‐chain positions of the loop region simultaneously according to the energy function selected by the user, and constructs a nonredundant ensemble of low energy loop conformations using filtering criteria. The method is illustrated with the DFIRE potential and DiSGro energy function for loops, and shown to be highly effective at discovering conformations with near‐native (or better) energy. Using the same energy function as the DiSGro algorithm, PETALS samples conformations with both lower RMSDs and lower energies. PETALS is also useful for assessing the accuracy of different energy functions. PETALS runs rapidly, requiring an average time cost of 10 minutes for a length 12 loop on a single 3.2 GHz processor core, comparable to the fastest existing de novo methods for generating an ensemble of conformations. Proteins 2017; 85:1402–1412. © 2017 Wiley Periodicals, Inc.     

Mimicking the action of folding chaperones by Hamiltonian replica-exchange molecular dynamics simulations: application in the refinement of de novo models

The efficiency of using a variant of Hamiltonian replica‐exchange molecular dynamics (Chaperone H‐replica‐exchange molecular dynamics [CH‐REMD]) for the refinement of protein structural models generated de novo is investigated. In CH‐REMD, the interaction between the protein and its environment, specifically, the electrostatic interaction between the protein and the solvating water, is varied leading to cycles of partial unfolding and refolding mimicking some aspects of folding chaperones. In 10 of the 15 cases examined, the CH‐REMD approach sampled structures in which the root‐mean‐square deviation (RMSD) of secondary structure elements (SSE‐RMSD) with respect to the experimental structure was more than 1.0 Å lower than the initial de novo model. In 14 of the 15 cases, the improvement was more than 0.5 Å. The ability of three different statistical potentials to identify near‐native conformations was also examined. Little correlation between the SSE‐RMSD of the sampled structures with respect to the experimental structure and any of the scoring functions tested was found. The most effective scoring function tested was the DFIRE potential. Using the DFIRE potential, the SSE‐RMSD of the best scoring structures was on average 0.3 Å lower than the initial model. Overall the work demonstrates that targeted enhanced‐sampling techniques such as CH‐REMD can lead to the systematic refinement of protein structural models generated de novo but that improved potentials for the identification of near‐native structures are still needed. Proteins 2012; © 2012 Wiley Periodicals, Inc.     

Protein loop modeling by using fragment assembly and analytical loop closure

Protein loops are often involved in important biological functions such as molecular recognition, signal transduction, or enzymatic action. The three dimensional structures of loops can provide essential information for understanding molecular mechanisms behind protein functions. In this article, we develop a novel method for protein loop modeling, where the loop conformations are generated by fragment assembly and analytical loop closure. The fragment assembly method reduces the conformational space drastically, and the analytical loop closure method finds the geometrically consistent loop conformations efficiently. We also derive an analytic formula for the gradient of any analytical function of dihedral angles in the space of closed loops. The gradient can be used to optimize various restraints derived from experiments or databases, for example restraints for preferential interactions between specific residues or for preferred backbone angles. We demonstrate that the current loop modeling method outperforms previous methods that employ residue‐based torsion angle maps or different loop closure strategies when tested on two sets of loop targets of lengths ranging from 4 to 12. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

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

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

Refinement of protein structures in explicit solvent

We present a CPU efficient protocol for refinement of protein structures in a thin layer of explicit solvent and energy parameters with completely revised dihedral angle terms. Our approach is suitable for protein structures determined by theoretical (e.g., homology modeling or threading) or experimental methods (e.g., NMR). In contrast to other recently proposed refinement protocols, we put a strong emphasis on consistency with widely accepted covalent parameters and computational efficiency. We illustrate the method for NMR structure calculations of three proteins: interleukin-4, ubiquitin, and crambin. We show a comparison of their structure ensembles before and after refinement in water with and without a force field energy term for the dihedral angles; crambin was also refined in DMSO. Our results demonstrate the significant improvement of structure quality by a short refinement in a thin layer of solvent. Further, they show that a dihedral angle energy term in the force field is beneficial for structure calculation and refinement. We discuss the optimal weight for the energy constant for the backbone angle omega and include an extensive discussion of meaning and relevance of the calculated validation criteria, in particular root mean square Z scores for covalent parameters such as bond lengths.     

Generation of accurate protein loop conformations through low-barrier molecular dynamics

Prediction and refinement of protein loop structures are important and challenging tasks for which no general solution has been found. In addition to the accuracy of scoring functions, the main problems reside in (1) insufficient statistical sampling and (2) crossing energy barriers that impede conformational rearrangements of the loop. We approach these two issues by using "low-barrier molecular dynamics," a combination of energy smoothing techniques. To address statistical sampling, locally enhanced sampling (LES) is used to produce multiple copies of the loop, thus improving statistics and reducing energy barriers. We introduce a novel extension of LES that can improve local sampling even further through hierarchical subdivision of copies. Even though LES reduces energy barriers, it cannot provide for crossing infinite barriers, which can be problematic when substantial rearrangement of residues is necessary. To permit this kind of loop residue repacking, a "soft-core" potential energy function is introduced, so that atomic overlaps are temporarily allowed. We tested this new combined methodology to a loop in anti-influenza antibody Fab 17/9 (7 residues long) and to another loop in the antiprogesterone antibody DB3 (8 residues). In both cases, starting from random conformations, we were able to locate correct loop structures (including sidechain orientations) with heavy-atom root-mean-square deviation (fit to the nonloop region) of approximately 1.1 A in Fab 17/9 and approximately 1.8 A in DB3. We show that the combination of LES and soft-core potential substantially improves sampling compared to regular molecular dynamics. Moreover, the sampling improvement obtained with this combined approach is significantly better than that provided by either of the two methods alone.     

High‐accuracy modeling of antibody structures by a search for minimum‐energy recombination of backbone fragments

Current methods for antibody structure prediction rely on sequence homology to known structures. Although this strategy often yields accurate predictions, models can be stereo‐chemically strained. Here, we present a fully automated algorithm, called AbPredict, that disregards sequence homology, and instead uses a Monte Carlo search for low‐energy conformations built from backbone segments and rigid‐body orientations that appear in antibody molecular structures. We find cases where AbPredict selects accurate loop templates with sequence identity as low as 10%, whereas the template of highest sequence identity diverges substantially from the query's conformation. Accordingly, in several cases reported in the recent Antibody Modeling Assessment benchmark, AbPredict models were more accurate than those from any participant, and the models' stereo‐chemical quality was consistently high. Furthermore, in two blind cases provided to us by crystallographers prior to structure determination, the method achieved <1.5 Ångstrom overall backbone accuracy. Accurate modeling of unstrained antibody structures will enable design and engineering of improved binders for biomedical research directly from sequence. Proteins 2016; 85:30–38. © 2016 Wiley Periodicals, Inc.     

Partial unfolding and refolding for structure refinement: A unified approach of geometric simulations and molecular dynamics

The most successful protein structure prediction methods to date have been template‐based modeling (TBM) or homology modeling, which predicts protein structure based on experimental structures. These high accuracy predictions sometimes retain structural errors due to incorrect templates or a lack of accurate templates in the case of low sequence similarity, making these structures inadequate in drug‐design studies or molecular dynamics simulations. We have developed a new physics based approach to the protein refinement problem by mimicking the mechanism of chaperons that rehabilitate misfolded proteins. The template structure is unfolded by selectively (targeted) pulling on different portions of the protein using the geometric based technique FRODA, and then refolded using hierarchically restrained replica exchange molecular dynamics simulations (hr‐REMD). FRODA unfolding is used to create a diverse set of topologies for surveying near native‐like structures from a template and to provide a set of persistent contacts to be employed during re‐folding. We have tested our approach on 13 previous CASP targets and observed that this method of folding an ensemble of partially unfolded structures, through the hierarchical addition of contact restraints (that is, first local and then nonlocal interactions), leads to a refolding of the structure along with refinement in most cases (12/13). Although this approach yields refined models through advancement in sampling, the task of blind selection of the best refined models still needs to be solved. Overall, the method can be useful for improved sampling for low resolution models where certain of the portions of the structure are incorrectly modeled. Proteins 2015; 83:2279–2292. © 2015 Wiley Periodicals, Inc.     

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

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

Application of statistical potentials to protein structure refinement from low resolution ab initio models

Recently ab initio protein structure prediction methods have advanced sufficiently so that they often assemble the correct low resolution structure of the protein. To enhance the speed of conformational search, many ab initio prediction programs adopt a reduced protein representation. However, for drug design purposes, better quality structures are probably needed. To achieve this refinement, it is natural to use a more detailed heavy atom representation. Here, as opposed to costly implicit or explicit solvent molecular dynamics simulations, knowledge-based heavy atom pair potentials were employed. By way of illustration, we tried to improve the quality of the predicted structures obtained from the ab initio prediction program TOUCHSTONE by three methods: local constraint refinement, reduced predicted tertiary contact refinement, and statistical pair potential guided molecular dynamics. Sixty-seven predicted structures from 30 small proteins (less than 150 residues in length) representing different structural classes (alpha, beta, alpha;/beta) were examined. In 33 cases, the root mean square deviation (RMSD) from native structures improved by more than 0.3 A; in 19 cases, the improvement was more than 0.5 A, and sometimes as large as 1 A. In only seven (four) cases did the refinement procedure increase the RMSD by more than 0.3 (0.5) A. For the remaining structures, the refinement procedures changed the structures by less than 0.3 A. While modest, the performance of the current refinement methods is better than the published refinement results obtained using standard molecular dynamics.