Enhanced Sampling of Coarse-Grained Transmembrane-Peptide Structure Formation from Hydrogen-Bond Replica Exchange

Protein structure formation in the membrane highlights a grand challenge of sampling in computer simulations, because kinetic traps and slow dynamics make it difficult to find the native state. Exploiting increased fluctuations at higher temperatures can help overcome free-energy barriers, provided the membrane’s structure remains stable. In this work, we apply Hamiltonian replica-exchange molecular dynamics, where we only tune the backbone hydrogen-bond strength to help reduce the propensity of long-lived misfolded states. Using a recently developed coarse-grained model, we illustrate the robustness of the method by folding different WALP transmembrane helical peptides starting from stretched, unstructured conformations. We show the efficiency of the method by comparing to simulations without enhanced sampling, achieving folding in one example after significantly longer simulation times. Analysis of the bilayer structure during folding provides insight into the local membrane deformation during helix formation as a function of chain length (from 16 to 23 residues). Finally, we apply our method to fold the 50-residue-long major pVIII coat protein (fd coat) of the filamentous fd bacteriophage. Our results agree well with experimental structures and atomistic simulations based on implicit membrane models, suggesting that our explicit CG folding protocol can serve as a starting point for better-refined atomistic simulations in a multiscale framework.     

Free energy landscape of protein folding in water: explicit vs. implicit solvent

The Generalized Born (GB) continuum solvent model is arguably the most widely used implicit solvent model in protein folding and protein structure prediction simulations; however, it still remains an open question on how well the model behaves in these large-scale simulations. The current study uses the beta-hairpin from C-terminus of protein G as an example to explore the folding free energy landscape with various GB models, and the results are compared to the explicit solvent simulations and experiments. All free energy landscapes are obtained from extensive conformation space sampling with a highly parallel replica exchange method. Because solvation model parameters are strongly coupled with force fields, five different force field/solvation model combinations are examined and compared in this study, namely the explicit solvent model: OPLSAA/SPC model, and the implicit solvent models: OPLSAA/SGB (Surface GB), AMBER94/GBSA (GB with Solvent Accessible Surface Area), AMBER96/GBSA, and AMBER99/GBSA. Surprisingly, we find that the free energy landscapes from implicit solvent models are quite different from that of the explicit solvent model. Except for AMBER96/GBSA, all other implicit solvent models find the lowest free energy state not the native state. All implicit solvent models show erroneous salt-bridge effects between charged residues, particularly in OPLSAA/SGB model, where the overly strong salt-bridge effect results in an overweighting of a non-native structure with one hydrophobic residue F52 expelled from the hydrophobic core in order to make better salt bridges. On the other hand, both AMBER94/GBSA and AMBER99/GBSA models turn the beta-hairpin in to an alpha-helix, and the alpha-helical content is much higher than the previously reported alpha-helices in an explicit solvent simulation with AMBER94 (AMBER94/TIP3P). Only AMBER96/GBSA shows a reasonable free energy landscape with the lowest free energy structure the native one despite an erroneous salt-bridge between D47 and K50. Detailed results on free energy contour maps, lowest free energy structures, distribution of native contacts, alpha-helical content during the folding process, NOE comparison with NMR, and temperature dependences are reported and discussed for all five models.     

Monte Carlo folding of trans-membrane helical peptides in an implicit generalized Born membrane

An efficient Monte Carlo (MC) algorithm using concerted backbone rotations is combined with a recently developed implicit membrane model to simulate the folding of the hydrophobic transmembrane domain M2TM of the M2 protein from influenza A virus and Sarcolipin at atomic resolution. The implicit membrane environment is based on generalized Born theory and has been calibrated against experimental data. The MC sampling has previously been used to fold several small polypeptides and been shown to be equivalent to molecular dynamics (MD). In combination with a replica exchange algorithm, M2TM is found to form continuous membrane spanning helical conformations for low temperature replicas. Sarcolipin is only partially helical, in agreement with the experimental NMR structures in lipid bilayers and detergent micelles. Higher temperature replicas exhibit a rapidly decreasing helicity, in agreement with expected thermodynamic behavior. To exclude the possibility of an erroneous helical bias in the simulations, the model is tested by sampling a synthetic Alanine-rich polypeptide of known helicity. The results demonstrate there is no overstabilization of helical conformations, indicating that the implicit model captures the essential components of the native membrane environment for M2TM and Sarcolipin.     

Force field influences in beta-hairpin folding simulations

All-atom force fields are now routinely used for more detailed understanding of protein folding mechanisms. However, it has been pointed out that use of all-atom force fields does not guarantee more accurate representations of proteins; in fact, sometimes it even leads to biased structural distributions. Indeed, several issues remain to be solved in force field developments, such as accurate treatment of implicit solvation for efficient conformational sampling and proper treatment of backbone interactions for secondary structure propensities. In this study, we first investigate the quality of several recently improved backbone interaction schemes in AMBER for folding simulations of a beta-hairpin peptide, and further study their influences on the peptide's folding mechanism. Due to the significant number of simulations needed for a thorough analysis of tested force fields, the implicit Poisson-Boltzmann solvent was used in all simulations. The chosen implicit solvent was found to be reasonable for studies of secondary structures based on a set of simulations of both alpha-helical and beta-hairpin peptides with the TIP3P explicit solvent as benchmark. Replica exchange molecular dynamics was also utilized for further efficient conformational sampling. Among the tested AMBER force fields, ff03 and a revised ff99 force field were found to produce structural and thermodynamic data in comparably good agreement with the experiment. However, detailed folding pathways, such as the order of backbone hydrogen bond zipping and the existence of intermediate states, are different between the two force fields, leading to force field-dependent folding mechanisms.     

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.     

De novo folding of membrane proteins: an exploration of the structure and NMR properties of the fd coat protein

De novo folding simulations of the major pVIII coat protein from filamentous fd bacteriophage, using a newly developed implicit membrane generalized Born model and replica-exchange molecular dynamics, are presented and discussed. The quality of the predicted structures, judged by comparison of the root-mean-square deviations of a room temperature ensemble of conformations from the replica-exchange simulations and experimental structures from both solid-state NMR in lipid bilayers and solution-phase NMR on the protein in micelles, was quite good, reinforcing the general quality of the folding simulations. The transmembrane helical segment of the protein was well defined in comparison with experiment and the amphipathic helical fragment remained at the membrane/aqueous phase boundary while undergoing significant conformational flexibility due to the loop connecting the two helical segments of the protein. Additional comparisons of computed solid-state NMR properties, the 15N chemical shift and 15N-1H dipolar coupling constants, showed semi-quantitative agreement with the corresponding measurements. These findings suggest an emerging potential for the de novo investigation of integral membrane peptides and proteins and a mechanism to assist experimental approaches to the characterization and structure determination of these important systems.     

Constant pH molecular dynamics of proteins in explicit solvent with proton tautomerism

pH is a ubiquitous regulator of biological activity, including protein‐folding, protein‐protein interactions, and enzymatic activity. Existing constant pH molecular dynamics (CPHMD) models that were developed to address questions related to the pH‐dependent properties of proteins are largely based on implicit solvent models. However, implicit solvent models are known to underestimate the desolvation energy of buried charged residues, increasing the error associated with predictions that involve internal ionizable residue that are important in processes like hydrogen transport and electron transfer. Furthermore, discrete water and ions cannot be modeled in implicit solvent, which are important in systems like membrane proteins and ion channels. We report on an explicit solvent constant pH molecular dynamics framework based on multi‐site λ‐dynamics (CPHMD^MSλD). In the CPHMD^MSλD framework, we performed seamless alchemical transitions between protonation and tautomeric states using multi‐site λ‐dynamics, and designed novel biasing potentials to ensure that the physical end‐states are predominantly sampled. We show that explicit solvent CPHMD^MSλD simulations model realistic pH‐dependent properties of proteins such as the Hen‐Egg White Lysozyme (HEWL), binding domain of 2‐oxoglutarate dehydrogenase (BBL) and N‐terminal domain of ribosomal protein L9 (NTL9), and the pK_a predictions are in excellent agreement with experimental values, with a RMSE ranging from 0.72 to 0.84 pK_a units. With the recent development of the explicit solvent CPHMD^MSλD framework for nucleic acids, accurate modeling of pH‐dependent properties of both major class of biomolecules—proteins and nucleic acids is now possible. Proteins 2014; 82:1319–1331. © 2013 Wiley Periodicals, Inc.     

Molecular dynamics simulations of peptides and proteins with amplified collective motions

We present a novel method that uses the collective modes obtained with a coarse-grained model/anisotropic network model to guide the atomic-level simulations. Based on this model, local collective modes can be calculated according to a single configuration in the conformational space of the protein. In the molecular dynamics simulations, the motions along the slowest few modes are coupled to a higher temperature by the weak coupling method to amplify the collective motions. This amplified-collective-motion (ACM) method is applied to two test systems. One is an S-peptide analog. We realized the refolding of the denatured peptide in eight simulations out of 10 using the method. The other system is bacteriophage T4 lysozyme. Much more extensive domain motions between the N-terminal and C-terminal domain of T4 lysozyme are observed in the ACM simulation compared to a conventional simulation. The ACM method allows for extensive sampling in conformational space while still restricting the sampled configurations within low energy areas. The method can be applied in both explicit and implicit solvent simulations, and may be further applied to important biological problems, such as long timescale functional motions, protein folding/unfolding, and structure prediction.     

Blind Test of Physics-Based Prediction of Protein Structures

We report here a multiprotein blind test of a computer method to predict native protein structures based solely on an all-atom physics-based force field. We use the AMBER 96 potential function with an implicit (GB/SA) model of solvation, combined with replica-exchange molecular-dynamics simulations. Coarse conformational sampling is performed using the zipping and assembly method (ZAM), an approach that is designed to mimic the putative physical routes of protein folding. ZAM was applied to the folding of six proteins, from 76 to 112 monomers in length, in CASP7, a community-wide blind test of protein structure prediction. Because these predictions have about the same level of accuracy as typical bioinformatics methods, and do not utilize information from databases of known native structures, this work opens up the possibility of predicting the structures of membrane proteins, synthetic peptides, or other foldable polymers, for which there is little prior knowledge of native structures. This approach may also be useful for predicting physical protein folding routes, non-native conformations, and other physical properties from amino acid sequences.     

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.     

Common Structural Transitions in Explicit-Solvent Simulations of Villin Headpiece Folding

Molecular dynamics simulations of protein folding can provide very high-resolution data on the folding process; however, due to computational challenges most studies of protein folding have been limited to small peptides, or made use of approximations such as Gō potentials or implicit solvent models. We have performed a set of molecular dynamics simulations totaling >50 μs on the villin headpiece subdomain, one of the most stable and fastest-folding naturally occurring proteins, in explicit solvent. We find that the wild-type villin headpiece reliably folds to a native conformation on timescales similar to experimentally observed folding, but that a fast folding double-norleucine mutant shows significantly more heterogeneous behavior. Along with other recent simulation studies, we note the occurrence of nonnative structures intermediates, which may yield a nativelike signal in the fluorescence measurements typically used to study villin folding. Based on the wild-type simulations, we propose alternative approaches to measure the formation of the native state.     

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.     

All-atom fast protein folding simulations: the villin headpiece

We provide a fast folding simulation using an all-atom solute, implicit solvent method that eliminates the need for treating solvent degrees of freedom. The folding simulations for the 36-residue villin headpiece exhibit close correspondence with the landmark all-atom explicit solvent molecular dynamics simulations by Duan and Kollman (Duan & Kollman, Science 1998;282:740-744; Duan, Wang, & Kollman, Proc Natl Acad Sci USA 1998;95:9897-9902). Our implicit solvent approach uses only an entry-level single CPU PC with comparable throughput ( approximately 4 nsec/day) to the DK supercomputer simulation. The native state is shown to be stable. Our 200-nsec folding trajectory agrees with the DK simulation in displaying a burst phase, a rapid initial shrinkage, a highly native-like binding site structure, and more.     

Estimating and interpreting migration of Amazonian forests using spatially implicit and semi‐explicit neutral models

With many sophisticated methods available for estimating migration, ecologists face the difficult decision of choosing for their specific line of work. Here we test and compare several methods, performing sanity and robustness tests, applying to large‐scale data and discussing the results and interpretation. Five methods were selected to compare for their ability to estimate migration from spatially implicit and semi‐explicit simulations based on three large‐scale field datasets from South America (Guyana, Suriname, French Guiana and Ecuador). Space was incorporated semi‐explicitly by a discrete probability mass function for local recruitment, migration from adjacent plots or from a metacommunity. Most methods were able to accurately estimate migration from spatially implicit simulations. For spatially semi‐explicit simulations, estimation was shown to be the additive effect of migration from adjacent plots and the metacommunity. It was only accurate when migration from the metacommunity outweighed that of adjacent plots, discrimination, however, proved to be impossible. We show that migration should be considered more an approximation of the resemblance between communities and the summed regional species pool. Application of migration estimates to simulate field datasets did show reasonably good fits and indicated consistent differences between sets in comparison with earlier studies. We conclude that estimates of migration using these methods are more an approximation of the homogenization among local communities over time rather than a direct measurement of migration and hence have a direct relationship with beta diversity. As betadiversity is the result of many (non)‐neutral processes, we have to admit that migration as estimated in a spatial explicit world encompasses not only direct migration but is an ecological aggregate of these processes. The parameter m of neutral models then appears more as an emerging property revealed by neutral theory instead of being an effective mechanistic parameter and spatially implicit models should be rejected as an approximation of forest dynamics.     

Solid-State NMR-Restrained Ensemble Dynamics of a Membrane Protein in Explicit Membranes

Solid-state NMR has been used to determine the structures of membrane proteins in native-like lipid bilayer environments. Most structure calculations based on solid-state NMR observables are performed using simulated annealing with restrained molecular dynamics and an energy function, where all nonbonded interactions are represented by a single, purely repulsive term with no contributions from van der Waals attractive, electrostatic, or solvation energy. To our knowledge, this is the first application of an ensemble dynamics technique performed in explicit membranes that uses experimental solid-state NMR observables to obtain the refined structure of a membrane protein together with information about its dynamics and its interactions with lipids. Using the membrane-bound form of the fd coat protein as a model membrane protein and its experimental solid-state NMR data, we performed restrained ensemble dynamics simulations with different ensemble sizes in explicit membranes. For comparison, a molecular dynamics simulation of fd coat protein was also performed without any restraints. The average orientation of each protein helix is similar to a structure determined by traditional single-conformer approaches. However, their variations are limited in the resulting ensemble of structures with one or two replicas, as they are under the strong influence of solid-state NMR restraints. Although highly consistent with all solid-state NMR observables, the ensembles of more than two replicas show larger orientational variations similar to those observed in the molecular dynamics simulation without restraints. In particular, in these explicit membrane simulations, Lys⁴⁰, residing at the C-terminal side of the transmembrane helix, is observed to cause local membrane curvature. Therefore, compared to traditional single-conformer approaches in implicit environments, solid-state NMR restrained ensemble simulations in explicit membranes readily characterize not only protein dynamics but also protein-lipid interactions in detail.     

Enhanced sampling simulations to construct free-energy landscape of protein–partner substrate interaction

Molecular dynamics (MD) simulations using all-atom and explicit solvent models provide valuable information on the detailed behavior of protein–partner substrate binding at the atomic level. As the power of computational resources increase, MD simulations are being used more widely and easily. However, it is still difficult to investigate the thermodynamic properties of protein–partner substrate binding and protein folding with conventional MD simulations. Enhanced sampling methods have been developed to sample conformations that reflect equilibrium conditions in a more efficient manner than conventional MD simulations, thereby allowing the construction of accurate free-energy landscapes. In this review, we discuss these enhanced sampling methods using a series of case-by-case examples. In particular, we review enhanced sampling methods conforming to trivial trajectory parallelization, virtual-system coupled multicanonical MD, and adaptive lambda square dynamics. These methods have been recently developed based on the existing method of multicanonical MD simulation. Their applications are reviewed with an emphasis on describing their practical implementation. In our concluding remarks we explore extensions of the enhanced sampling methods that may allow for even more efficient sampling.     

Secondary Structure Propensities in Peptide Folding Simulations: A Systematic Comparison of Molecular Mechanics Interaction Schemes

We present a systematic study directed toward the secondary structure propensity and sampling behavior in peptide folding simulations with eight different molecular dynamics force-field variants in explicit solvent. We report on the combinational result of force field, water model, and electrostatic interaction schemes and compare to available experimental characterization of five studied model peptides in terms of reproduced structure and dynamics. The total simulation time exceeded 18 μs and included simulations that started from both folded and extended conformations. Despite remaining sampling issues, a number of distinct trends in the folding behavior of the peptides emerged. Pronounced differences in the propensity of finding prominent secondary structure motifs in the different applied force fields suggest that problems point in particular to the balance of the relative stabilities of helical and extended conformations.     

Comparison of the potentials of mean force for alanine tetrapeptide between integral equation theory and simulation.

The dielectrically consistent reference interaction site model (DRISM) integral equation theory is applied to determine the potential of mean force (PMF) for an alanine tetramer. A stochastic dynamics simulation of the alanine tetramer using this PMF is then compared with an explicit water molecular dynamics simulation. In addition, comparison is also done with simulations using other solvent models like the extended reference interaction site model (XRISM) theory, constant dielectric and linear distance-dependent dielectric models. The results show that the DRISM method offers a fairly accurate and computationally inexpensive alternative to explicit water simulations for studies on small peptides.