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.     

Application of biasing‐potential replica‐exchange simulations for loop modeling and refinement of proteins in explicit solvent

Comparative or homology modeling of a target protein based on sequence similarity to a protein with known structure is widely used to provide structural models of proteins. Depending on the target‐template similarity these model structures may contain regions of limited structural accuracy. In principle, molecular dynamics (MD) simulations can be used to refine protein model structures and also to model loop regions that connect structurally conserved regions but it is limited by the currently accessible simulation time scales. A recently developed biasing potential replica exchange (BP‐REMD) method was used to refine loops and complete decoy protein structures at atomic resolution including explicit solvent. In standard REMD simulations several replicas of a system are run in parallel at different temperatures allowing exchanges at preset time intervals. In a BP‐REMD simulation replicas are controlled by various levels of a biasing potential to reduce the energy barriers associated with peptide backbone dihedral transitions. The method requires much fewer replicas for efficient sampling compared with T‐REMD. Application of the approach to several protein loops indicated improved conformational sampling of backbone dihedral angle of loop residues compared to conventional MD simulations. BP‐REMD refinement simulations on several test cases starting from decoy structures deviating significantly from the native structure resulted in final structures in much closer agreement with experiment compared to conventional MD simulations. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

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.     

Influence of 8-Oxoguanosine on the Fine Structure of DNA Studied with Biasing-Potential Replica Exchange Simulations

Chemical modification or radiation can cause DNA damage, which plays a crucial role for mutagenesis of DNA, carcinogenesis, and aging. DNA damage can also alter the fine structure of DNA that may serve as a recognition signal for DNA repair enzymes. A new, advanced sampling replica-exchange method has been developed to specifically enhance the sampling of conformational substates in duplex DNA during molecular dynamics (MD) simulations. The approach employs specific biasing potentials acting on pairs of pseudodihedral angles of the nucleic acid backbone that are added in the replica simulations to promote transitions of the most common substates of the DNA backbone. The sampled states can exchange with a reference simulation under the control of the original force field. The application to 7,8-dihydro-8oxo-guanosine, one of the most common oxidative damage in DNA indicated better convergence of sampled states during 10 ns simulations compared to 20 times longer standard MD simulations. It is well suited to study systematically the fine structure and dynamics of large nucleic acids under realistic conditions, including explicit solvent and ions. The biasing potential-replica exchange MD simulations indicated significant differences in the population of nucleic acid backbone substates in the case of 7,8-dihydro-8oxo-guanosine compared to a regular guanosine in the same sequence context. This concerns both the ratio of the B-DNA substates B_I and B_II associated with the backbone dihedral angles ε and ζ but also coupled changes in the backbone dihedral angles α and γ. Such differences may play a crucial role in the initial recognition of damaged DNA by repair enzymes.     

Effects of force fields on the conformational and dynamic properties of amyloid β(1‐40) dimer explored by replica exchange molecular dynamics simulations

The conformational space and structural ensembles of amyloid beta (Aβ) peptides and their oligomers in solution are inherently disordered and proven to be challenging to study. Optimum force field selection for molecular dynamics (MD) simulations and the biophysical relevance of results are still unknown. We compared the conformational space of the Aβ(1‐40) dimers by 300 ns replica exchange MD simulations at physiological temperature (310 K) using: the AMBER‐ff99sb‐ILDN, AMBER‐ff99sb*‐ILDN, AMBER‐ff99sb‐NMR, and CHARMM22* force fields. Statistical comparisons of simulation results to experimental data and previously published simulations utilizing the CHARMM22* and CHARMM36 force fields were performed. All force fields yield sampled ensembles of conformations with collision cross sectional areas for the dimer that are statistically significantly larger than experimental results. All force fields, with the exception of AMBER‐ff99sb‐ILDN (8.8 ± 6.4%) and CHARMM36 (2.7 ± 4.2%), tend to overestimate the α‐helical content compared to experimental CD (5.3 ± 5.2%). Using the AMBER‐ff99sb‐NMR force field resulted in the greatest degree of variance (41.3 ± 12.9%). Except for the AMBER‐ff99sb‐NMR force field, the others tended to under estimate the expected amount of β‐sheet and over estimate the amount of turn/bend/random coil conformations. All force fields, with the exception AMBER‐ff99sb‐NMR, reproduce a theoretically expected β‐sheet‐turn‐β‐sheet conformational motif, however, only the CHARMM22* and CHARMM36 force fields yield results compatible with collapse of the central and C‐terminal hydrophobic cores from residues 17‐21 and 30‐36. Although analyses of essential subspace sampling showed only minor variations between force fields, secondary structures of lowest energy conformers are different.     

Structural Characterization of N-WASP Domain V Using MD Simulations with NMR and SAXS Data

Because of their large conformational heterogeneity, structural characterization of intrinsically disordered proteins (IDPs) is very challenging using classical experimental methods alone. In this study, we use NMR and small-angle x-ray scattering (SAXS) data with multiple molecular dynamics (MD) simulations to describe the conformational ensemble of the fully disordered verprolin homology domain of the neural Aldrich syndrome protein involved in the regulation of actin polymerization. First, we studied several back-calculation software of SAXS scattering intensity and optimized the adjustable parameters to accurately calculate the SAXS intensity from an atomic structure. We also identified the most appropriate force fields for MD simulations of this IDP. Then, we analyzed four conformational ensembles of neural Aldrich syndrome protein verprolin homology domain, two generated with the program flexible-meccano with or without NMR-derived information as input and two others generated by MD simulations with two different force fields. These four conformational ensembles were compared to available NMR and SAXS data for validation. We found that MD simulations with the AMBER-03w force field and the TIP4P/2005s water model are able to correctly describe the conformational ensemble of this 67-residue IDP at both local and global level.     

Temperature‐accelerated molecular dynamics gives insights into globular conformations sampled in the free state of the AC catalytic domain

The catalytic domain of the adenyl cyclase (AC) toxin from Bordetella pertussis is activated by interaction with calmodulin (CaM), resulting in cAMP overproduction in the infected cell. In the X‐ray crystallographic structure of the complex between AC and the C terminal lobe of CaM, the toxin displays a markedly elongated shape. As for the structure of the isolated protein, experimental results support the hypothesis that more globular conformations are sampled, but information at atomic resolution is still lacking. Here, we use temperature‐accelerated molecular dynamics (TAMD) simulations to generate putative all‐atom models of globular conformations sampled by CaM‐free AC. As collective variables, we use centers of mass coordinates of groups of residues selected from the analysis of standard molecular dynamics (MD) simulations. Results show that TAMD allows extended conformational sampling and generates AC conformations that are more globular than in the complexed state. These structures are then refined via energy minimization and further unrestrained MD simulations to optimize inter‐domain packing interactions, thus resulting in the identification of a set of hydrogen bonds present in the globular conformations. Proteins 2014; 82:2483–2496. © 2014 Wiley Periodicals, Inc.     

Unconstrained enhanced sampling for free energy calculations of biomolecules: a review

Abstract

Free energy calculations are central to understanding the structure, dynamics and function of biomolecules. Yet insufficient sampling of biomolecular configurations is often regarded as one of the main sources of error. Many enhanced sampling techniques have been developed to address this issue. Notably, enhanced sampling methods based on biasing collective variables (CVs), including the widely used umbrella sampling, adaptive biasing force and metadynamics, have been discussed in a recent excellent review (Abrams and Bussi, Entropy, 2014). Here, we aim to review enhanced sampling methods that do not require predefined system-dependent CVs for biomolecular simulations and as such do not suffer from the hidden energy barrier problem as encountered in the CV-biasing methods. These methods include, but are not limited to, replica exchange/parallel tempering, self-guided molecular/Langevin dynamics, essential energy space random walk and accelerated molecular dynamics. While it is overwhelming to describe all details of each method, we provide a summary of the methods along with the applications and offer our perspectives. We conclude with challenges and prospects of the unconstrained enhanced sampling methods for accurate biomolecular free energy calculations.     

Improved side‐chain torsion potentials for the Amber ff99SB protein force field

Recent advances in hardware and software have enabled increasingly long molecular dynamics (MD) simulations of biomolecules, exposing certain limitations in the accuracy of the force fields used for such simulations and spurring efforts to refine these force fields. Recent modifications to the Amber and CHARMM protein force fields, for example, have improved the backbone torsion potentials, remedying deficiencies in earlier versions. Here, we further advance simulation accuracy by improving the amino acid side‐chain torsion potentials of the Amber ff99SB force field. First, we used simulations of model alpha‐helical systems to identify the four residue types whose rotamer distribution differed the most from expectations based on Protein Data Bank statistics. Second, we optimized the side‐chain torsion potentials of these residues to match new, high‐level quantum‐mechanical calculations. Finally, we used microsecond‐timescale MD simulations in explicit solvent to validate the resulting force field against a large set of experimental NMR measurements that directly probe side‐chain conformations. The new force field, which we have termed Amber ff99SB‐ILDN, exhibits considerably better agreement with the NMR data. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Ensemble MD simulations restrained via crystallographic data: Accurate structure leads to accurate dynamics

Currently, the best existing molecular dynamics (MD) force fields cannot accurately reproduce the global free‐energy minimum which realizes the experimental protein structure. As a result, long MD trajectories tend to drift away from the starting coordinates (e.g., crystallographic structures). To address this problem, we have devised a new simulation strategy aimed at protein crystals. An MD simulation of protein crystal is essentially an ensemble simulation involving multiple protein molecules in a crystal unit cell (or a block of unit cells). To ensure that average protein coordinates remain correct during the simulation, we introduced crystallography‐based restraints into the MD protocol. Because these restraints are aimed at the ensemble‐average structure, they have only minimal impact on conformational dynamics of the individual protein molecules. So long as the average structure remains reasonable, the proteins move in a native‐like fashion as dictated by the original force field. To validate this approach, we have used the data from solid‐state NMR spectroscopy, which is the orthogonal experimental technique uniquely sensitive to protein local dynamics. The new method has been tested on the well‐established model protein, ubiquitin. The ensemble‐restrained MD simulations produced lower crystallographic R factors than conventional simulations; they also led to more accurate predictions for crystallographic temperature factors, solid‐state chemical shifts, and backbone order parameters. The predictions for ¹⁵N relaxation rates are at least as accurate as those obtained from conventional simulations. Taken together, these results suggest that the presented trajectories may be among the most realistic protein MD simulations ever reported. In this context, the ensemble restraints based on high‐resolution crystallographic data can be viewed as protein‐specific empirical corrections to the standard force fields.     

Close correspondence between the motions from principal component analysis of multiple HIV-1 protease structures and elastic network modes

The large number of available HIV-1 protease structures provides a remarkable sampling of conformations of the different conformational states, which can be viewed as direct structural information about the dynamics of the HIV-1 protease. After structure matching, we apply principal component analysis (PCA) to obtain the important apparent motions for both bound and unbound structures. There are significant similarities between the first few key motions and the first few low-frequency normal modes calculated from a static representative structure with an elastic network model (ENM), strongly suggesting that the variations among the observed structures and the corresponding conformational changes are facilitated by the low-frequency, global motions intrinsic to the structure. Similarities are also found when the approach is applied to an NMR ensemble, as well as to molecular dynamics (MD) trajectories. Thus, a sufficiently large number of experimental structures can directly provide important information about protein dynamics, but ENM can also provide similar sampling of conformations.     

A flexible docking scheme to explore the binding selectivity of PDZ domains

Modeling of protein binding site flexibility in molecular docking is still a challenging problem due to the large conformational space that needs sampling. Here, we propose a flexible receptor docking scheme: A dihedral restrained replica exchange molecular dynamics (REMD), where we incorporate the normal modes obtained by the Elastic Network Model (ENM) as dihedral restraints to speed up the search towards correct binding site conformations. To our knowledge, this is the first approach that uses ENM modes to bias REMD simulations towards binding induced fluctuations in docking studies. In our docking scheme, we first obtain the deformed structures of the unbound protein as initial conformations by moving along the binding fluctuation mode, and perform REMD using the ENM modes as dihedral restraints. Then, we generate an ensemble of multiple receptor conformations (MRCs) by clustering the lowest replica trajectory. Using ROSETTA LIGAND , we dock ligands to the clustered conformations to predict the binding pose and affinity. We apply this method to postsynaptic density‐95/Dlg/ZO‐1 (PDZ) domains; whose dynamics govern their binding specificity. Our approach produces the lowest energy bound complexes with an average ligand root mean square deviation of 0.36 Å. We further test our method on (i) homologs and (ii) mutant structures of PDZ where mutations alter the binding selectivity. In both cases, our approach succeeds to predict the correct pose and the affinity of binding peptides. Overall, with this approach, we generate an ensemble of MRCs that leads to predict the binding poses and specificities of a protein complex accurately.     

Headgroup Conformations of Phospholipids from Molecular Dynamics Simulation: Sampling Challenges and Comparison to Experiment

The preferred conformations of the glycerol region of a phospholipid have been explored using replica exchange molecular dynamics (MD) simulations and compared with the results of standard MD approaches and with experiment. We found that due to isomerization rates in key torsions that are slow on the timescale of atomistic MD simulations, standard MD is not able to produce accurate equilibrium conformer distributions from reasonable trajectory lengths (e.g., on the 100 ns) timescale. Replica exchange MD, however, results in quite efficient sampling due to the rapid increase in isomerization rate with temperature. The equilibrium distributions obtained from replica exchange MD have been compared with the results of experimental nuclear magnetic resonance observations. This comparison suggests that the sampling approach demonstrated here is a valuable tool that can be used in evaluating force fields for molecular simulation of lipids.     

Predicting large-scale conformational changes in proteins using energy-weighted normal modes

We report the development of a method to improve the sampling of protein conformational space in molecular simulations. It is shown that a principal component analysis of energy-weighted normal modes in Cartesian coordinates can be used to extract vectors suitable for describing the dynamics of protein substructures. The method can operate with either atomistic or user-defined coarse-grained models of protein structure. An implicit reverse coarse-graining allows the dynamics of all-atoms to be recovered when a coarse-grained model is used. For an external test set of four proteins, it is shown that the new method is more successful than normal mode analysis in describing the large-scale conformational changes observed on ligand binding. The method has potential applications in protein-ligand and protein-protein docking and in biasing molecular dynamics simulations.     

163 Enhanced sampling of peptides and proteins with a new biasing replica exchange method

Classical MD simulations (cMD) are limited by the sampling of relevant states of the peptides. Replica exchange (REMD) methods aim to search the conformational space of proteins more efficiently (reviewed in Ostermeir & Zacharias, 2013). We have developed a Hamiltonian REMD method that takes advantage of an intrinsic property of proteins, the specific Φ ? dihedral angle combinations along the polymer backbone. By employing a coupled two-dimensional biasing potential the energy barriers along the polymer backbone are reduced more effectively than by a previous approach based on a one-D biasing potential (Kannan & Zacharias, 2007). Thus, adjacent amino acids along the polymers backbone can easily switch between favourable regions in the Ramachandran plot. Additionally, energy barriers of rotameric states of amino acid side chains of proteins are also biased in the replica runs. The method improves the sampling of conformational substates of proteins at a modest number of replicas (nine replicas in the standard set-up with one replica running without biasing potential) compared to much larger numbers necessary in the case of standard temperature (T)-REMD simulations. A further improvement is achieved by a dynamical adjustment of the penalty potential levels in the replicas such that high exchange rates and improved mixing of conformations between different replicas are guaranteed. The biasing potential (BP)-REMD method turns out to be suitable to speed up both the folding of spaghetti-like test peptides and the refinement of loop decoy structures. Starting from extended structures, an α-helical oligo-alanine and β-hairpin chignolin and the Trp-cage protein fold more rapidly in near-native structures than in cMD simulations. The BP-REMD simulations not only accelerate the folding process of test proteins but also enlarge the variety of sampled configurations in conformational space. Since flexible parts of the protein can be penalized selectively, this method provides a precise tool to investigate regions of interest of the protein.     

Simulated annealing coupled replica exchange molecular dynamics—An efficient conformational sampling method

Molecular dynamics simulated annealing (SA-MD) simulations are frequently used for refinement and optimization of peptide and protein structures. Depending on the simulation conditions and simulation length SA-MD simulations can be trapped in locally stable conformations far from the global optimum. As an alternative replica exchange molecular dynamics (RexMD) simulations can be used which allow exchanges between high and low simulation temperatures at all stages of the simulation. A significant drawback of RexMD simulations is, however, the rapid increase of the replica number with increasing system size to cover a desired temperature range. A combined SA-MD and RexMD approach termed SA-RexMD is suggested that employs a small number of replicas (4) and starts initially with a set of high simulation temperatures followed by gradual cooling of the set of temperatures until a target temperature has been reached. The protocol has been applied for the folding of several peptide systems and for the refinement of protein model structures. In all the cases, the SA-RexMD method turned out to be significantly more efficient in reaching low energy structures and also structures close to experiment compared to continuous MD simulations at the target temperature and to SA-MD simulations at the same computational demand. The approach is well suited for applications in structure refinement and for systematic force field improvement.     

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.     

Highly sampled tetranucleotide and tetraloop motifs enable evaluation of common RNA force fields

Recent modifications and improvements to standard nucleic acid force fields have attempted to fix problems and issues that have been observed as longer timescale simulations have become routine. Although previous work has shown the ability to fold the UUCG stem–loop structure, until now no group has attempted to quantify the performance of current force fields using highly converged structural populations of the tetraloop conformational ensemble. In this study, we report the use of multiple independent sets of multidimensional replica exchange molecular dynamics (M-REMD) simulations with different initial conditions to generate well-converged conformational ensembles for the tetranucleotides r(GACC) and r(CCCC), as well as the larger UUCG tetraloop motif. By generating what is to our knowledge the most complete RNA structure ensembles reported to date for these systems, we remove the coupling between force field errors and errors due to incomplete sampling, providing a comprehensive comparison between current top-performing MD force fields for RNA. Of the RNA force fields tested in this study, none demonstrate the ability to correctly identify the most thermodynamically stable structure for all three systems. We discuss the deficiencies present in each potential function and suggest areas where improvements can be made. The results imply that although “short” (nsec-μsec timescale) simulations may stay close to their respective experimental structures and may well reproduce experimental observables, inevitably the current force fields will populate alternative incorrect structures that are more stable than those observed via experiment.     

A coupling of homology modeling with multiple molecular dynamics simulation for identifying representative conformation of GPCR structures: a case study on human bombesin receptor subtype-3

In this study, a computational pipeline was therefore devised to overcome homology modeling (HM) bottlenecks. The coupling of HM with molecular dynamics (MD) simulation is useful in that it tackles the sampling deficiency of dynamics simulations by providing good-quality initial guesses for the native structure. Indeed, HM also relaxes the severe requirement of force fields to explore the huge conformational space of protein structures. In this study, the interaction between the human bombesin receptor subtype-3 and MK-5046 was investigated integrating HM, molecular docking, and MD simulations. To improve conformational sampling in typical MD simulations of GPCRs, as in other biomolecules, multiple trajectories with different initial conditions can be employed rather than a single long trajectory. Multiple MD simulations of human bombesin receptor subtype-3 with different initial atomic velocities are applied to sample conformations in the vicinity of the structure generated by HM. The backbone atom conformational space distribution of replicates is analyzed employing principal components analysis. As a result, the averages of structural and dynamic properties over the twenty-one trajectories differ significantly from those obtained from individual trajectories.     

Advanced replica-exchange sampling to study the flexibility and plasticity of peptides and proteins

Molecular dynamics (MD) simulations are ideally suited to investigate protein and peptide plasticity and flexibility simultaneously at high spatial (atomic) and high time resolution. However, the applicability is still limited by the force field accuracy and by the maximum simulation time that can be routinely achieved in current MD simulations. In order to improve the sampling the replica-exchange (REMD) methodology has become popular and is now the most widely applied advanced sampling approach. Many variants of the REMD method have been designed to reduce the computational demand or to enhance sampling along specific sets of conformational variables. An overview on recent methodological advances and discussion of specific aims and advantages of the approaches will be given. Applications in the area of free energy simulations and advanced sampling of intrinsically disordered peptides and proteins will also be discussed. This article is part of a Special Issue entitled: The emerging dynamic view of proteins: Protein plasticity in allostery, evolution and self-assembly.