Hamiltonian Replica Exchange Method Research Articles

Identifying the Template for Oligomer to Fibril Conversion for Amyloid-β (1-42) Oligomers using Hamiltonian Replica Exchange Molecular Dynamics.

The toxicity of amyloid-β (Aβ) oligomers has been known to be higher compared to mature fibrils. Yet the presence of plaques in Alzheimer's disease patients indicates the significance of oligomer to fibril conversion for Aβ aggregates. In this study, we investigate Aβ13-42 oligomers having two to five peptide chains using extensive all-atom molecular dynamics simulations to identify the on- or off-pathway intermediates in fibril formation pathway. Hamiltonian replica exchange method through solute tempering (REST2) has been employed to explore the different structures attained by these aggregates. Using intra-chain and inter-chain contacts as reaction coordinates, we obtain the free energy surface for the Aβ13-42 oligomers. Consequently, their stable conformations and structural features have been identified. The found conformations belonging to most probable structures possess both parallel and anti-parallel β-sheets, characteristic of on- and off-pathway intermediates, respectively. Further, we have measured the tendency to form fibril like interactions among the β-sheet forming residues. Our analysis finds that residues 30-36 possess higher tendency to form fibril like contacts among all the residues. While we find stronger interaction among residues 30-36, these amino acids are also found to be more shielded from water compared to others. With previous experimental studies finding these residues to be more crucial for the stability of Aβ42 oligomers, we propose that interactions within this patch could trigger seed formation that leads to conversion of on-pathway oligomers into disease relevant fibrils.

Does Hamiltonian Replica Exchange via Lambda-Hopping Enhance the Sampling in Alchemical Free Energy Calculations?

In the context of computational drug design, we examine the effectiveness of the enhanced sampling techniques in state-of-the-art free energy calculations based on alchemical molecular dynamics simulations. In a paradigmatic molecule with competition between conformationally restrained E and Z isomers whose probability ratio is strongly affected by the coupling with the environment, we compare the so-called -hopping technique to the Hamiltonian replica exchange methods assessing their convergence behavior as a function of the enhanced sampling protocols (number of replicas, scaling factors, simulation times). We found that the pure -hopping, commonly used in solvation and binding free energy calculations via alchemical free energy perturbation techniques, is ineffective in enhancing the sampling of the isomeric states, exhibiting a pathological dependence on the initial conditions. Correct sampling can be restored in -hopping simulation by the addition of a “hot-zone” scaling factor to the -stratification (FEP+ approach), provided that the additive hot-zone scaling factors are tuned and optimized using preliminary ordinary replica-exchange simulation of the end-states.

Binding-induced functional-domain motions in the Argonaute characterized by adaptive advanced sampling.

Argonaute proteins in combination with short microRNA (miRNAs) can target mRNA molecules for translation inhibition or degradation and play a key role in many regulatory processes. The miRNAs act as guide RNAs that associate with Argonaute and the complementary mRNA target region. The complex formation results in activation of Argonaute and specific cleavage of the target mRNA. Both the binding and activation processes involve essential domain rearrangements of functional importance. For the Thermus Thermophilus Argonaute (TtAgo) system guide-bound (binary) and guide/target-bound (ternary) complexes are known but how the binding of guide and target mediate domain movements is still not understood. We have studied the Argonaute domain motion in apo and guide/target bound states using Molecular Dynamics simulations and a Hamiltonian replica exchange (H-REMD) method that employs a specific biasing potential to accelerate domain motions. The H-REMD technique indicates sampling of a much broader distribution of domain arrangements both in the apo as well as binary and ternary complexes compared to regular MD simulations. In the apo state domain arrangements corresponding to more compact (closed) states are mainly sampled which undergo an opening upon guide and guide/target binding. Whereas only limited overlap in domain geometry between apo and bound states was found, a larger similarity in the domain distribution is observed for the simulations of binary and ternary complexes. Comparative simulations on ternary complexes with 15 or 16 base pairs (bp) formed between guide and target strands (instead of 14) resulted in dissociation of the 3'-guide strand from the PAZ domain and domain rearrangement. This agrees with the experimental observation that guide-target pairing beyond 14 bps is required for activation and gives a mechanistic explanation for the experimentally observed activation process.

Coupling Coarse-Grained to Fine-Grained Models via Hamiltonian Replica Exchange.

The energy landscape of biomolecular systems contains many local minima that are separated by high energy barriers. Sampling this landscape in molecular dynamics simulations is a challenging task and often requires the use of enhanced sampling techniques. Here, we increase the sampling efficiency by coupling the fine-grained (FG) GROMOS force field to the coarse-grained (CG) Martini force field via the Hamiltonian replica exchange method (HREM). We tested the efficiency of this procedure using a lutein/octane system. In traditional simulations, cis–trans transitions of lutein are barely observed due to the high energy barrier separating these states. However, many of these transitions are sampled with our HREM scheme. The proposed method offers new possibilities for enhanced sampling of biomolecular conformations, making use of CG models without compromising the accuracy of the FG model.

Influence of Calcium Binding on Conformations and Motions of Anionic Polyamino Acids. Effect of Side Chain Length.

Investigation of the effect of CaCl2 salt on conformations of two anionic poly(amino acids) with different side chain lengths, poly-(α-l glutamic acid) (PGA) and poly-(α-l aspartic acid) (PASA), was performed by atomistic molecular dynamics (MD) simulations. The simulations were performed using both unbiased MD and the Hamiltonian replica exchange (HRE) method. The results show that at low CaCl2 concentration adsorption of Ca2+ ions lead to a significant chain size reduction for both PGA and PASA. With the increase in concentration, the chains sizes partially recover due to electrostatic repulsion between the adsorbed Ca2+ ions. Here, the side chain length becomes important. Due to the longer side chain and its ability to distance the charged groups with adsorbed ions from both each other and the backbone, PGA remains longer in the collapsed state as the CaCl2 concentration is increased. The analysis of the distribution of the mineral ions suggests that both poly(amino acids) should induce the formation of mineral with the same structure of the crystal cell.

Global Dynamics of Yeast Hsp90 Middle and C-Terminal Dimer Studied by Advanced Sampling Simulations.

The Hsp90 protein complex is one of the most abundant molecular chaperone proteins that assists in folding of a variety of client proteins. During its functional cycle it undergoes large domain rearrangements coupled to the hydrolysis of ATP and association or dissociation of domain interfaces. In order to better understand the domain dynamics comparative Molecular Dynamics (MD) simulations of a sub-structure of Hsp90, the dimer formed by the middle (M) and C-terminal domain (C), were performed. Since this MC dimer lacks the ATP-binding N-domain it allows studying global motions decoupled from ATP binding and hydrolysis. Conventional (c)MD simulations starting from several different closed and open conformations resulted in only limited sampling of global motions. However, the application of a Hamiltonian Replica exchange (H-REMD) method based on the addition of a biasing potential extracted from a coarse-grained elastic network description of the system allowed much broader sampling of domain motions than the cMD simulations. With this multiscale approach it was possible to extract the main directions of global motions and to obtain insight into the molecular mechanism of the global structural transitions of the MC dimer.

Prediction of CB[8] host-guest binding free energies in SAMPL6 using the double-decoupling method.

This study reports the results of binding free energy calculations for CB[8] host-guest systems in the SAMPL6 blind challenge (receipt ID 3z83m). Force-field parameters were developed specific for each of host and guest molecules to improve configurational sampling. We used quantum mechanical (QM) implicit solvent calculations and QM force matching to determine non-bonded (partial atomic charges) and bonded terms, respectively. Free energy calculations were carried out using the double-decoupling method (DDM) combined with Hamiltonian replica exchange method (HREM) and Bennett acceptance ratio (BAR) method. The root mean square error (RMSE) of the predicted values using DDM with respect to the experimental results was 4.32kcal/mol. The coefficient of determination (R2) and Kendall rank coefficient (τ) were 0.49 and 0.52, respectively, highest of all submissions. In addition, these were compared to the results obtained by umbrella sampling (US) and weighted histogram analysis method (WHAM). Overall, DDM achieved a higher prediction accuracy than the US method. Results are discussed in terms of parameterization and free energy simulations.

Exploring Cryptic Pockets Formation in Targets of Pharmaceutical Interest with SWISH.

Cryptic (hidden) pockets are sites that are not visible on unliganded target proteins' structures and only become apparent when a ligand binds. They might provide a valid alternative to classical binding sites in otherwise "undruggable" targets, but their hidden nature makes it difficult to use standard structure-based or computer-aided drug discovery approaches. Our group recently developed a Hamiltonian replica-exchange method (sampling water interfaces through scaled Hamiltonians or SWISH) that improves the sampling of hydrophobic cavities by scaling the interactions between water molecules and protein atoms. Here, we discuss further improvements to SWISH and its combination with fragment probe simulations. We tested the robustness and general applicability of the improved approach in a variety of pharmaceutically relevant targets. The chosen proteins: NPC2, p38α, LfrR, and hPNMT, represent a set of diversified and interesting targets harboring nontrivial cryptic binding sites. In all cases, the updated version of our algorithm efficiently explored the cryptic sites.

Communication: Self-assembly of a model supramolecular polymer studied by replica exchange with solute tempering

Conventional molecular-dynamics (cMD) simulation has a well-known limitation in accessible time and length scales, and thus various enhanced sampling techniques have been proposed to alleviate the problem. In this paper, we explore the utility of replica exchange with solute tempering (REST) (i.e., a variant of Hamiltonian replica exchange methods) to simulate the self-assembly of a supramolecular polymer in explicit solvent and compare the performance with temperature-based replica exchange MD (T-REMD) as well as cMD. As a test system, we consider a relatively simple all-atom model of supramolecular polymerization (namely, benzene-1,3,5-tricarboxamides in methylcyclohexane solvent). Our results show that both REST and T-REMD are able to predict highly ordered polymer structures with helical H-bonding patterns, in contrast to cMD which completely fails to obtain such a structure for the present model. At the same time, we have also experienced some technical challenge (i.e., aggregation-dispersion transition and the resulting bottleneck for replica traversal), which is illustrated numerically. Since the computational cost of REST scales more moderately than T-REMD, we expect that REST will be useful for studying the self-assembly of larger systems in solution with enhanced rearrangement of monomers.

Computational scheme for pH-dependent binding free energy calculation with explicit solvent.

We present a computational scheme to compute the pH-dependence of binding free energy with explicit solvent. Despite the importance of pH, the effect of pH has been generally neglected in binding free energy calculations because of a lack of accurate methods to model it. To address this limitation, we use a constant-pH methodology to obtain a true ensemble of multiple protonation states of a titratable system at a given pH and analyze the ensemble using the Bennett acceptance ratio (BAR) method. The constant pH method is based on the combination of enveloping distribution sampling (EDS) with the Hamiltonian replica exchange method (HREM), which yields an accurate semi-grand canonical ensemble of a titratable system. By considering the free energy change of constraining multiple protonation states to a single state or releasing a single protonation state to multiple states, the pH dependent binding free energy profile can be obtained. We perform benchmark simulations of a host-guest system: cucurbit[7]uril (CB[7]) and benzimidazole (BZ). BZ experiences a large pKa shift upon complex formation. The pH-dependent binding free energy profiles of the benchmark system are obtained with three different long-range interaction calculation schemes: a cutoff, the particle mesh Ewald (PME), and the isotropic periodic sum (IPS) method. Our scheme captures the pH-dependent behavior of binding free energy successfully. Absolute binding free energy values obtained with the PME and IPS methods are consistent, while cutoff method results are off by 2 kcal mol(-1) . We also discuss the characteristics of three long-range interaction calculation methods for constant-pH simulations.

Enhanced conformational sampling using replica exchange with concurrent solute scaling and hamiltonian biasing realized in one dimension.

Replica exchange (REX) is a powerful computational tool for overcoming the quasi-ergodic sampling problem of complex molecular systems. Recently, several multidimensional extensions of this method have been developed to realize exchanges in both temperature and biasing potential space or the use of multiple biasing potentials to improve sampling efficiency. However, increased computational cost due to the multidimensionality of exchanges becomes challenging for use on complex systems under explicit solvent conditions. In this study, we develop a one-dimensional (1D) REX algorithm to concurrently combine the advantages of overall enhanced sampling from Hamiltonian solute scaling and the specific enhancement of collective variables using Hamiltonian biasing potentials. In the present Hamiltonian replica exchange method, termed HREST-BP, Hamiltonian solute scaling is applied to the solute subsystem, and its interactions with the environment to enhance overall conformational transitions and biasing potentials are added along selected collective variables associated with specific conformational transitions, thereby balancing the sampling of different hierarchical degrees of freedom. The two enhanced sampling approaches are implemented concurrently allowing for the use of a small number of replicas (e.g., 6 to 8) in 1D, thus greatly reducing the computational cost in complex system simulations. The present method is applied to conformational sampling of two nitrogen-linked glycans (N-glycans) found on the HIV gp120 envelope protein. Considering the general importance of the conformational sampling problem, HREST-BP represents an efficient procedure for the study of complex saccharides, and, more generally, the method is anticipated to be of general utility for the conformational sampling in a wide range of macromolecular systems.

Constant pH Molecular Dynamics in Explicit Solvent with Enveloping Distribution Sampling and Hamiltonian Exchange

We present a new computational approach for constant pH simulations in explicit solvent based on the combination of the enveloping distribution sampling (EDS) and Hamiltonian replica exchange (HREX) methods. Unlike constant pH methods based on variable and continuous charge models, our method is based on discrete protonation states. EDS generates a hybrid Hamiltonian of different protonation states. A smoothness parameter s is used to control the heights of energy barriers of the hybrid-state energy landscape. A small s value facilitates state transitions by lowering energy barriers. Replica exchange between EDS potentials with different s values allows us to readily obtain a thermodynamically accurate ensemble of multiple protonation states with frequent state transitions. The analysis is performed with an ensemble obtained from an EDS Hamiltonian without smoothing, s = ∞, which strictly follows the minimum energy surface of the end states. The accuracy and efficiency of this method is tested on aspartic...

Enhanced Conformational Sampling of Carbohydrates using Biasing Potential and Solute Tempering Replica Exchange: Application to the N-glycan on the HIV gp120 Envelope Protein

Conformational sampling of complex molecular systems is always a challenge in computer simulations. To tackle this problem, a range of enhanced sampling methods have been developed. However, each method typically only shows distinct advantages in specific systems. Therefore, new approaches aim to combine the complementarity of different enhanced sampling algorithms to achieve a better performance. In this study, we propose a new algorithm to combine the advantages of two Hamiltonian replica exchange methods designed to improve sampling of specific degrees of freedom using biasing potentials and of global conformational properties, including solute-solvent interactions via solute tempering.1-2 The new method produces improved sampling for polysaccharides with coupled linkages, including branch points. The method is applied to N-glycans found on the HIV gp120 envelope protein that show potential application in the design of HIV vaccines.

Dimerization process of amyloid-β(29-42) studied by the Hamiltonian replica-permutation molecular dynamics simulations.

The amyloid-β peptides form amyloid fibrils which are associated with Alzheimer's disease. Amyloid-β(29-42) is its C-terminal fragment and a critical determinant of the amyloid formation rate. This fragment forms the amyloid fibril by itself. However, the fragment conformation in the fibril has yet to be determined. The oligomerization process including the dimerization process is also still unknown. The dimerization process corresponds to an early process of the amyloidogenesis. In order to investigate the dimerization process and conformations, we applied the Hamiltonian replica-permutation method, which is a better alternative to the Hamiltonian replica-exchange method, to two amyloid-β(29-42) molecules in explicit water solvent. At the first step of the dimerization process, two amyloid-β(29-42) molecules came close to each other and had intermolecular side chain contacts. When two molecules had the intermolecular side chain contacts, the amyloid-β(29-42) tended to have intramolecular secondary structures, especially β-hairpin structures. The two molecules had intermolecular β-bridge structures by coming much closer at the second step of the dimerization process. Formation of these intermolecular β-bridge structures was induced by the β-hairpin structures. The intermolecular β-sheet structures elongated at the final step. Structures of the amyloid-β(29-42) in the monomer and dimer states are also shown with the free-energy landscapes, which were obtained by performing efficient sampling in the conformational space in our simulations.

Constant pH Molecular Dynamics in Explicit Solvent with Enveloping Distribution Sampling and Hamiltonian Exchange.

We present a new computational approach for constant pH simulations in explicit solvent based on the combination of the enveloping distribution sampling (EDS) and Hamiltonian replica exchange (HREX) methods. Unlike constant pH methods based on variable and continuous charge models, our method is based on discrete protonation states. EDS generates a hybrid Hamiltonian of different protonation states. A smoothness parameter s is used to control the heights of energy barriers of the hybrid-state energy landscape. A small s value facilitates state transitions by lowering energy barriers. Replica exchange between EDS potentials with different s values allows us to readily obtain a thermodynamically accurate ensemble of multiple protonation states with frequent state transitions. The analysis is performed with an ensemble obtained from an EDS Hamiltonian without smoothing, s = ∞, which strictly follows the minimum energy surface of the end states. The accuracy and efficiency of this method is tested on aspartic acid, lysine, and glutamic acid, which have two protonation states, a histidine with three states, a four-residue peptide with four states, and snake cardiotoxin with eight states. The pKa values estimated with the EDS-HREX method agree well with the experimental pKa values. The mean absolute errors of small benchmark systems range from 0.03 to 0.17 pKa units, and those of three titratable groups of snake cardiotoxin range from 0.2 to 1.6 pKa units. This study demonstrates that EDS-HREX is a potent theoretical framework, which gives the correct description of multiple protonation states and good calculated pKa values.

Evaluation of enhanced sampling provided by accelerated molecular dynamics with Hamiltonian replica exchange methods.

Many problems studied via molecular dynamics require accurate estimates of various thermodynamic properties, such as the free energies of different states of a system, which in turn requires well-converged sampling of the ensemble of possible structures. Enhanced sampling techniques are often applied to provide faster convergence than is possible with traditional molecular dynamics simulations. Hamiltonian replica exchange molecular dynamics (H-REMD) is a particularly attractive method, as it allows the incorporation of a variety of enhanced sampling techniques through modifications to the various Hamiltonians. In this work, we study the enhanced sampling of the RNA tetranucleotide r(GACC) provided by H-REMD combined with accelerated molecular dynamics (aMD), where a boosting potential is applied to torsions, and compare this to the enhanced sampling provided by H-REMD in which torsion potential barrier heights are scaled down to lower force constants. We show that H-REMD and multidimensional REMD (M-REMD) combined with aMD does indeed enhance sampling for r(GACC), and that the addition of the temperature dimension in the M-REMD simulations is necessary to efficiently sample rare conformations. Interestingly, we find that the rate of convergence can be improved in a single H-REMD dimension by simply increasing the number of replicas from 8 to 24 without increasing the maximum level of bias. The results also indicate that factors beyond replica spacing, such as round trip times and time spent at each replica, must be considered in order to achieve optimal sampling efficiency.

Adaptive Biasing Combined with Hamiltonian Replica Exchange to Improve Umbrella Sampling Free Energy Simulations.

The accurate calculation of potentials of mean force for ligand-receptor binding is one of the most important applications of molecular simulation techniques. Typically, the separation distance between ligand and receptor is chosen as a reaction coordinate along which a PMF can be calculated with the aid of umbrella sampling (US) techniques. In addition, restraints can be applied on the relative position and orientation of the partner molecules to reduce accessible phase space. An approach combining such phase space reduction with flattening of the free energy landscape and configurational exchanges has been developed, which significantly improves the convergence of PMF calculations in comparison with standard umbrella sampling. The free energy surface along the reaction coordinate is smoothened by iteratively adapting biasing potentials corresponding to previously calculated PMFs. Configurations are allowed to exchange between the umbrella simulation windows via the Hamiltonian replica exchange method. The application to a DNA molecule in complex with a minor groove binding ligand indicates significantly improved convergence and complete reversibility of the sampling along the pathway. The calculated binding free energy is in excellent agreement with experimental results. In contrast, the application of standard US resulted in large differences between PMFs calculated for association and dissociation pathways. The approach could be a useful alternative to standard US for computational studies on biomolecular recognition processes.

Adaptive Biasing Combined with Hamiltonian Replica Exchange to Improve Umbrella Sampling Free Energy Simulations

The calculation of binding free energies using potential of mean force based techniques is an important application of molecular simulations. Typically, a potential of mean force (PMF) along the separation distance between two binding molecules is calculated using umbrella sampling (US). Convergence can be improved by introducing restraints on the relative position and orientation of the molecules as well as on their configurational freedom. Application of such umbrella sampling protocol on DNA in complex with the minor-groove binding ligand furamidine failed to yield converged results within reasonable simulation time. Significant energy barriers and tightly bound water molecules in the DNA minor groove that only occasionally exchanged with the bulk appeared to be a major reason for insufficient convergence. However, convergence could be greatly improved by a combination of standard phase space reduction techniques with flattening of the free energy landscape and configurational exchanges using the Hamiltonian replica exchange method. The approach uses an iteratively adapting biasing potential that corresponds to a previously calculated PMF and smoothens the free energy surface in combination with replica exchanges along the reaction coordinate. In contrast to standard US, the combined method resulted in rapid convergence of calculated free energy changes along the separation distance coordinate and excellent agreement of dissociation and association calculations with experimental results.

Hamiltonian replica-permutation method and its applications to an alanine dipeptide and amyloid-β(29-42) peptides

We propose the Hamiltonian replica-permutation method (RPM) (or multidimensional RPM) for molecular dynamics and Monte Carlo simulations, in which parameters in the Hamiltonian are permuted among more than two replicas with the Suwa-Todo algorithm. We apply the Coulomb RPM, which is one of realization of the Hamiltonian RPM, to an alanine dipeptide and to two amyloid-β(29-42) molecules. The Hamiltonian RPM realizes more efficient sampling than the Hamiltonian replica-exchange method. We illustrate the protein misfolding funnel of amyloid-β(29-42) and reveal its dimerization pathways.

Transformation of a design peptide between the α-helix and β-hairpin structures using a helix-strand replica-exchange molecular dynamics simulation

We investigated the transformation between the α-helix and β-hairpin structures of an 18-residue design peptide, whose sequence is INYWLAHAKAGYIVHWTA. This peptide has both α-helix and β-hairpin structures in aqueous solution. For this purpose, we proposed the helix-strand replica-exchange method. This is one of the Hamiltonian replica-exchange methods in which we exchange parameters for umbrella potentials to enhance the α-helix or β-strand structure formation. We performed an all-atom helix-strand replica-exchange molecular dynamics (MD) simulation of this peptide in explicit water solvent with five replicas. Because the suitable umbrella potential was applied, the helix-strand replica-exchange MD simulation reproduced conformations closer to experimental conformations than a temperature replica-exchange MD simulation when the same numbers of the replicas were used, while the temperature replica-exchange MD simulation does not require bias along any specific order parameter. We calculated its free-energy landscape and revealed the transformation pathways between the α-helix and β-hairpin structures and the folding pathways from an extended structure. Although the fractions of the α-helix and β-hairpin structures are less than those obtained by the experiment, the free-energy difference between the two structures is calculated to be almost zero, which agrees with the experimental results.