Replica-Permutation Method with the Suwa-Todo Algorithm beyond the Replica-Exchange Method

Why Is Arginine the Only Amino Acid That Inhibits Polyglutamine Monomers from Taking on Toxic Conformations?

Polyglutamine (polyQ) diseases are devastating neurodegenerative disorders characterized by abnormal expansion of glutamine repeats within specific proteins. The aggregation of polyQ proteins is a critical pathological hallmark of these diseases. Arginine was identified as a promising inhibitory compound because it prevents polyQ-protein monomers from forming intra- and intermolecular β-sheet structures and hinders polyQ proteins from aggregating to form oligomers. Such an aggregation inhibitory effect was not observed in other amino acids. However, the underlying molecular mechanism of the aggregation inhibition and the factors that differentiate arginine from other amino acids, in terms of the inhibition of the polyQ-protein aggregation, remain poorly understood. Here, we performed replica-permutation molecular dynamics simulations to elucidate the molecular mechanism by which arginine inhibits the formation of the intramolecular β-sheet structure of a polyQ monomer. We found that the intramolecular β-sheet structure with more than four β-bridges of the polyQ monomer with arginine is more unstable than without any ligand and with lysine. We also found that arginine has 1.6-2.1 times more contact with polyQ than lysine. In addition, we revealed that arginine forms more hydrogen bonds with the main chain of the polyQ monomer than lysine. More hydrogen bonds formed between arginine and polyQ inhibit polyQ from forming the long intramolecular β-sheet structure. It is known that intramolecular β-sheet structure enhances intermolecular β-sheet structure between proteins. These effects are thought to be the reason for the inhibition of polyQ aggregation. This study provides insights into the molecular events underlying arginine's inhibition of polyQ-protein aggregation.

Current State of Open Source Force Fields in Protein-Ligand Binding Affinity Predictions

In drug discovery, the in silico prediction of binding affinity is one of the major means to prioritize compounds for synthesis. Alchemical relative binding free energy (RBFE) calculations based on molecular dynamics (MD) simulations are nowadays a popular approach for the accurate affinity ranking of compounds. MD simulations rely on empirical force field parameters, which strongly influence the accuracy of the predicted affinities. Here, we evaluate the ability of six different small-molecule force fields to predict experimental protein-ligand binding affinities in RBFE calculations on a set of 598 ligands and 22 protein targets. The public force fields OpenFF Parsley and Sage, GAFF, and CGenFF show comparable accuracy, while OPLS3e is significantly more accurate. However, a consensus approach using Sage, GAFF, and CGenFF leads to accuracy comparable to OPLS3e. While Parsley and Sage are performing comparably based on aggregated statistics across the whole dataset, there are differences in terms of outliers. Analysis of the force field reveals that improved parameters lead to significant improvement in the accuracy of affinity predictions on subsets of the dataset involving those parameters. Lower accuracy can not only be attributed to the force field parameters but is also dependent on input preparation and sampling convergence of the calculations. Especially large perturbations and nonconverged simulations lead to less accurate predictions. The input structures, Gromacs force field files, as well as the analysis Python notebooks are available on GitHub.

Perspective for Molecular Dynamics Simulation Studies of Amyloid-β Aggregates

The cause of Alzheimer's disease is related to aggregates such as oligomers and amyloid fibrils consisting of amyloid-β (Aβ) peptides. Molecular dynamics (MD) simulation studies have been conducted to understand the molecular mechanism of the formation and disruption of Aβ aggregates. In this Perspective, the MD simulation studies are classified into four categories, focusing on the target systems: aggregation of Aβ peptides in bulk solution, Aβ aggregation at the interface, aggregation inhibitor against Aβ peptides, and nonequilibrium MD simulation of Aβ aggregates. MD simulation studies in these categories are first reviewed. Future perspectives in each category are then presented. Finally, the overall perspective is presented on how MD simulations of Aβ aggregates can be utilized for developing Alzheimer's disease treatment.

An interoperable implementation of collective-variable based enhanced sampling methods in extended phase space within the OpenMM package

Collective variable (CV)-based enhanced sampling techniques are widely used today for accelerating barrier-crossing events in molecular simulations. A class of these methods, which includes temperature accelerated molecular dynamics (TAMD)/driven-adiabatic free energy dynamics (d-AFED), unified free energy dynamics (UFED), and temperature accelerated sliced sampling (TASS), uses an extended variable formalism to achieve quick exploration of conformational space. These techniques are powerful, as they enhance the sampling of a large number of CVs simultaneously compared to other techniques. Extended variables are kept at a much higher temperature than the physical temperature by ensuring adiabatic separation between the extended and physical subsystems and employing rigorous thermostatting. In this work, we present a computational platform to perform extended phase space enhanced sampling simulations using the open-source molecular dynamics engine OpenMM. The implementation allows users to have interoperability of sampling techniques, as well as employ state-of-the-art thermostats and multiple time-stepping. This work also presents protocols for determining the critical parameters and procedures for reconstructing high-dimensional free energy surfaces. As a demonstration, we present simulation results on the high dimensional conformational landscapes of the alanine tripeptide in vacuo, tetra-N-methylglycine (tetra-sarcosine) peptoid in implicit solvent, and the Trp-cage mini protein in explicit water.

SEVI Inhibits Aβ Amyloid Aggregation by Capping the β-Sheet Elongation Edges

Inhibiting the aggregation of amyloid peptides with endogenous peptides has broad interest due to their intrinsically high biocompatibility and low immunogenicity. Here, we investigated the inhibition mechanism of the prostatic acidic phosphatase fragment SEVI (semen-derived enhancer of viral infection) against Aβ42 fibrillization using atomistic discrete molecular dynamic simulations. Our result revealed that SEVI was intrinsically disordered with dynamic formation of residual helices. With a high positive net charge, the self-aggregation tendency of SEVI was weak. Aβ42 had a strong aggregation propensity by readily self-assembling into β-sheet-rich aggregates. SEVI preferred to interact with Aβ42, rather than SEVI themselves. In the heteroaggregates, Aβ42 mainly adopted β-sheets buried inside and capped by SEVI in the outer layer. SEVI could bind to various Aβ aggregation species─including monomers, dimers, and proto-fibrils─by capping the exposed β-sheet elongation edges. The aggregation processes Aβ42 from the formation of oligomers to conformational nucleation into fibrils and fibril growth should be inhibited as their β-sheet elongation edges are being occupied by the highly charged SEVI. Overall, our computational study uncovered the molecular mechanism of experimentally observed inhibition of SEVI against Aβ42 aggregation, providing novel insights into the development of therapeutic strategies against Alzheimer's disease.

Inhibition Effect and Molecular Mechanisms of Quercetin on the Aβ42 Dimer: A Molecular Dynamics Simulation Study

Amyloid-β (Aβ) dimer as the smallest oligomer has recently been drawing attention due to its neurotoxicity, transient nature, and heterogeneity. The inhibition of Aβ dimer's aggregation is the key to primary intervention of Alzheimer's disease. Previous experimental studies have reported that quercetin, the widespread polyphenolic constituent of multiple fruits and vegetables, can hamper the formation of Aβ protofibrils and disaggregate Aβ fibrils. However, the molecular mechanisms of quercetin in the suppression of the Aβ(1-42) dimer's conformational changes still remain elusive. In this work, to investigate the inhibitory mechanisms of quercetin molecules on the Aβ(1-42) dimer, an Aβ(1-42) dimer based on monomeric the Aβ(1-42) peptide with enriched coil structures is constructed. The early molecular mechanisms of quercetin molecules on inhibiting the Aβ(1-42) dimer at two different Aβ42-to-quercetin molar ratios (1:5 and 1:10) are explored via all-atom molecular dynamics simulations. The results indicate that quercetin molecules can impede the configurational change of the Aβ(1-42) dimer. The interactions and the binding affinity between the Aβ(1-42) dimer and quercetin molecules in the Aβ42 dimer + 20 quercetin system are stronger in comparison with that in the Aβ42 dimer + 10 quercetin system. Our work may be helpful in developing new drug candidates for preventing the conformational transition and further aggregation of the Aβ dimer.

Acceleration of generalized replica exchange with solute tempering simulations of large biological systems on massively parallel supercomputer

Generalized replica exchange with solute tempering (gREST) is one of the enhanced sampling algorithms for proteins or other systems with rugged energy landscapes. Unlike the replica-exchange molecular dynamics (REMD) method, solvent temperatures are the same in all replicas, while solute temperatures are different and are exchanged frequently between replicas for exploring various solute structures. Here, we apply the gREST scheme to large biological systems containing over one million atoms using a large number of processors in a supercomputer. First, communication time on a multi-dimensional torus network is reduced by matching each replica to MPI processors optimally. This is applicable not only to gREST but also to other multi-copy algorithms. Second, energy evaluations, which are necessary for the multistate bennet acceptance ratio (MBAR) method for free energy estimations, are performed on-the-fly during the gREST simulations. Using these two advanced schemes, we observed 57.72 ns/day performance in 128-replica gREST calculations with 1.5 million atoms system using 16,384 nodes in Fugaku. These schemes implemented in the latest version of GENESIS software could open new possibilities to answer unresolved questions on large biomolecular complex systems with slow conformational dynamics.

Dissecting the Molecular Mechanisms of the Co-Aggregation of Aβ40 and Aβ42 Peptides: A REMD Simulation Study

The aggregation of amyloid-β protein (Aβ) into oligomers and amyloid fibrils is closely related to Alzheimer's disease (AD). Aβ40 and Aβ42, as two most prominent isoforms of Aβ peptides, can cross-interact with each other and form co-aggregates, which affect the progression of the disease. However, the molecular determinants underlying Aβ40 and Aβ42 cross-interaction and the structural details of their co-oligomers remain elusive. Herein, we performed all-atom explicit-solvent replica exchange molecular dynamics simulations on Aβ40-Aβ42 heterogeneous and Aβ40/Aβ42 homogeneous dimer systems to dissect the co-aggregation mechanisms of the two isoforms. Our results show that the interpeptide main-chain interaction of Aβ40-Aβ42 is stronger than that of Aβ40-Aβ40 and Aβ42-Aβ42. The positions of hotspot residues in heterodimers and homodimers display high similarity, implying similar molecular recognition sites for both cross-interaction and self-interaction. Contact maps of Aβ40-Aβ42 heterodimers reveal that residue pairs crucial for cross-interaction are mostly located in the C-terminal hydrophobic regions of Aβ40 and Aβ42 peptides. Conformational analysis shows that Aβ40 and Aβ42 monomers can co-assemble into β-sheet-rich heterodimers with shorter β-sheets than those in homodimers, which is decremental to monomer addition. Similar molecular recognition sites and β-sheet distribution of Aβ40 and Aβ42 peptides are observed in heterodimers and homodimers, which may provide the molecular basis for the two isoforms' co-aggregation and cross-seeding. Our work dissects the co-aggregation mechanisms of Aβ40 and Aβ42 peptides at the atomic level, which will help for in-depth understanding of the cross-talk between the two Aβ isoforms and the pathogenesis of AD.

Ingenuity in performing replica permutation: How to order the state labels for improving sampling efficiency

In the replica-permutation method, an advanced version of the replica-exchange method, all combinations of replicas and parameters are considered for parameter permutation, and a list of all the combinations is prepared. Here, we report that the temperature transition probability depends on how the list is created, especially in replica permutation with solute tempering (RPST). We found that the transition probabilities decrease at large replica indices when the combinations are sequentially assigned to the state labels as in the originally proposed list. To solve this problem, we propose to modify the list by randomly assigning the combinations to the state labels. We performed molecular dynamics simulations of amyloid-β(16-22) peptides using RPST with the "randomly assigned" list (RPST-RA) and RPST with the "sequentially assigned" list (RPST-SA). The results show the decreases in the transition probabilities in RPST-SA are eliminated, and the sampling efficiency is improved in RPST-RA.

Optimal Replica-Exchange Molecular Simulations in Combination with Evolution Strategies

We have incorporated Evolution Strategies into the Replica-Exchange Monte Carlo simulation method to predict the phase behavior of several example fluids. The replica-exchange method allows one system to exchange temperatures with its neighbors to search for the most stable structure relatively efficiently in a single simulation. However, if the temperature intervals of the replicas are not positioned carefully, there is an issue that local exchange does not occur. Our results for a simple Lennard-Jones fluid and the liquid-crystal Yukawa model demonstrate the utility of the approach when compared to conventional methods. When Evolution Strategies were applied to the Replica-Exchange Monte Carlo simulation, the problem of a significant localized decrease in exchange probability near the phase transition was avoided. By obtaining the optimal temperature intervals, the system efficiently traverses a broader parameter space with a small number of replicas. This is equivalent to accelerating molecular simulations with limited computational resources and can be useful when attempting to predict the phase behavior of complex systems.

Computer simulation of molecular recognition in biomolecular system: from in silico screening to generalized ensembles

Prediction of ligand-receptor complex structure is important in both the basic science and the industry such as drug discovery. We report various computation molecular docking methods: fundamental in silico (virtual) screening, ensemble docking, enhanced sampling (generalized ensemble) methods, and other methods to improve the accuracy of the complex structure. We explain not only the merits of these methods but also their limits of application and discuss some interaction terms which are not considered in the in silico methods. In silico screening and ensemble docking are useful when one focuses on obtaining the native complex structure (the most thermodynamically stable complex). Generalized ensemble method provides a free-energy landscape, which shows the distribution of the most stable complex structure and semi-stable ones in a conformational space. Also, barriers separating those stable structures are identified. A researcher should select one of the methods according to the research aim and depending on complexity of the molecular system to be studied.

Key Residue for Aggregation of Amyloid-β Peptides

It is known that oligomers of amyloid-β (Aβ) peptide are associated with Alzheimer's disease. Aβ has two isoforms: Aβ40 and Aβ42. Although the difference between Aβ40 and Aβ42 is only two additional C-terminal residues, Aβ42 aggregates much faster than Aβ40. It is unknown what role the C-terminal two residues play in accelerating aggregation. Since Aβ42 is more toxic than Aβ40, its oligomerization process needs to be clarified. Moreover, clarifying the differences between the oligomerization processes of Aβ40 and Aβ42 is essential to elucidate the key factors of oligomerization. Therefore, to investigate the dimerization process, which is the early oligomerization process, Hamiltonian replica-permutation molecular dynamics simulations were performed for Aβ40 and Aβ42. We identified a key residue, Arg5, for the Aβ42 dimerization. The two additional residues in Aβ42 allow the C-terminus to form contact with Arg5 because of the electrostatic attraction between them, and this contact stabilizes the β-hairpin. This β-hairpin promotes dimer formation through the intermolecular β-bridges. Thus, we examined the effects of amino acid substitutions of Arg5, thereby confirming that the mutations remarkably suppressed the aggregation of Aβ42. Moreover, the mutations of Arg5 suppressed the Aβ40 aggregation. It was found by analyzing the simulations that Arg5 is important for Aβ40 to form intermolecular contacts. Thus, it was clarified that the role of Arg5 in the oligomerization process varies due to the two additional C-terminal residues.

State-of-the-Art Molecular Dynamics Simulation Studies of RNA-Dependent RNA Polymerase of SARS-CoV-2

Molecular dynamics (MD) simulations are powerful theoretical methods that can reveal biomolecular properties, such as structure, fluctuations, and ligand binding, at the level of atomic detail. In this review article, recent MD simulation studies on these biomolecular properties of the RNA-dependent RNA polymerase (RdRp), which is a multidomain protein, of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) are presented. Although the tertiary structures of RdRps in SARS-CoV-2 and SARS-CoV are almost identical, the RNA synthesis activity of RdRp of SARS-CoV is higher than SARS-CoV-2. Recent MD simulations observed a difference in the dynamic properties of the two RdRps, which may cause activity differences. RdRp is also a drug target for Coronavirus disease 2019 (COVID-19). Nucleotide analogs, such as remdesivir and favipiravir, are considered to be taken up by RdRp and inhibit RNA replication. Recent MD simulations revealed the recognition mechanism of RdRp for these drug molecules and adenosine triphosphate (ATP). The ligand-recognition ability of RdRp decreases in the order of remdesivir, favipiravir, and ATP. As a typical recognition process, it was found that several lysine residues of RdRp transfer these ligand molecules to the binding site such as a “bucket brigade.” This finding will contribute to understanding the mechanism of the efficient ligand recognition by RdRp. In addition, various simulation studies on the complexes of SARS-CoV-2 RdRp with several nucleotide analogs are reviewed, and the molecular mechanisms by which these compounds inhibit the function of RdRp are discussed. The simulation studies presented in this review will provide useful insights into how nucleotide analogs are recognized by RdRp and inhibit the RNA replication.

Molecular Dynamics Simulation Studies on the Aggregation of Amyloid-β Peptides and Their Disaggregation by Ultrasonic Wave and Infrared Laser Irradiation

Alzheimer’s disease is understood to be caused by amyloid fibrils and oligomers formed by aggregated amyloid-β (Aβ) peptides. This review article presents molecular dynamics (MD) simulation studies of Aβ peptides and Aβ fragments on their aggregation, aggregation inhibition, amyloid fibril conformations in equilibrium, and disruption of the amyloid fibril by ultrasonic wave and infrared laser irradiation. In the aggregation of Aβ, a β-hairpin structure promotes the formation of intermolecular β-sheet structures. Aβ peptides tend to exist at hydrophilic/hydrophobic interfaces and form more β-hairpin structures than in bulk water. These facts are the reasons why the aggregation is accelerated at the interface. We also explain how polyphenols, which are attracting attention as aggregation inhibitors of Aβ peptides, interact with Aβ. An MD simulation study of the Aβ amyloid fibrils in equilibrium is also presented: the Aβ amyloid fibril has a different structure at one end from that at the other end. The amyloid fibrils can be destroyed by ultrasonic wave and infrared laser irradiation. The molecular mechanisms of these amyloid fibril disruptions are also explained, particularly focusing on the function of water molecules. Finally, we discuss the prospects for developing treatments for Alzheimer’s disease using MD simulations.

Replica permutation with solute tempering for molecular dynamics simulation and its application to the dimerization of amyloid-β fragments

We propose the replica permutation with solute tempering (RPST) by combining the replica-permutation method (RPM) and the replica exchange with solute tempering (REST). Temperature permutations are performed among more than two replicas in RPM, whereas temperature exchanges are performed between two replicas in the replica-exchange method (REM). The temperature transition in RPM occurs more efficiently than in REM. In REST, only the temperatures of the solute region, the solute temperatures, are exchanged to reduce the number of replicas compared to REM. Therefore, RPST is expected to be an improved method taking advantage of these methods. For comparison, we applied RPST, REST, RPM, and REM to two amyloid-β(16–22) peptides in explicit water. We calculated the transition ratio and the number of tunneling events in the temperature space and the number of dimerization events of amyloid-β(16–22) peptides. The results indicate that, in RPST, the number of replicas necessary for frequent random walks in the temperature and conformational spaces is reduced compared to the other three methods. In addition, we focused on the dimerization process of amyloid-β(16–22) peptides. The RPST simulation with a relatively small number of replicas shows that the two amyloid-β(16–22) peptides form the intermolecular antiparallel β-bridges due to the hydrophilic side-chain contact between Lys and Glu and hydrophobic side-chain contact between Leu, Val, and Phe, which stabilizes the dimer of the peptides.

All-Atom Molecular Dynamics Simulation Methods for the Aggregation of Protein and Peptides: Replica Exchange/Permutation and Nonequilibrium Simulations

Protein aggregates are associated with more than 40 serious human diseases. To understand the formation mechanism of protein aggregates at atomic level, all-atom molecular dynamics (MD) simulation is a powerful computational tool. In this chapter, we review the all-atom MD simulation methods that are useful for study on the protein aggregation. We first explain conventional MD simulation methods in physical statistical ensembles, such as the canonical and isothermal-isobaric ensembles. We then describe the generalized-ensemble algorithms such as replica-exchange and replica-permutation MD methods. These methods can overcome a difficulty, in which simulations tend to get trapped in local-minimum free-energy states. Finally we explain the nonequilibrium MD method. Some simulation results based on these methods are also presented.

Dynamic properties of SARS-CoV and SARS-CoV-2 RNA-dependent RNA polymerases studied by molecular dynamics simulations

One of the promising drug targets against COVID-19 is an RNA-dependent RNA polymerase (RdRp) of SARS-CoV-2. The tertiary structures of the SARS-CoV-2 and SARS-CoV RdRps are almost the same. However, the RNA-synthesizing activity of the SARS-CoV RdRp is higher than that of the SARS-CoV-2 RdRp. We performed molecular dynamics simulations and found differences in their dynamic properties. In the SARS-CoV RdRp, motifs A-G, which form the active site, are up to 63% closer to each other. We also observed cooperative domain motion in the SARS-CoV RdRp. Such dynamic differences may cause the activity differences between the two RdRps.

Dimerization of α-Synuclein Fragments Studied by Isothermal-Isobaric Replica-Permutation Molecular Dynamics Simulation

Aggregates and fibrils of intrinsically disordered α-synuclein are associated with Parkinson's disease. Within a non-amyloid β component (NAC) spanning from the 61st to the 95th residue of α-synuclein, an 11-residue segment called NACore (₆₈GAVVTGVTAVA₇₈) is an essential region for both fibril formation and cytotoxicity. Although NACore peptides alone are known to form aggregates and amyloid fibrils, the mechanisms of aggregation and fibrillation remain unknown. This study investigated the dimerization process of NACore peptides as the initial stage of the aggregation and fibrillation processes. We performed an isothermal-isobaric replica-permutation molecular dynamics simulation, which is one of the efficient sampling methods, for the two NACore peptides in explicit water over 96 μs. The simulation succeeded in sampling a variety of dimer structures. An analysis of secondary structure revealed that most of the NACore dimers form intermolecular β-bridges. In particular, more antiparallel β-bridges were observed than parallel β-bridges. We also found that intramolecular secondary structures such as α-helix and antiparallel β-bridge are stabilized in the pre-dimer state. However, we identified that the intermolecular β-bridges tend to form directly between residues with no specific structure rather than via the intramolecular β-bridges. This is because the NACore peptides still have a low propensity to form the intramolecular secondary structures even though they are stabilized in the pre-dimer state.

Promotion and Inhibition of Amyloid-β Peptide Aggregation: Molecular Dynamics Studies

Aggregates of amyloid-β (Aβ) peptides are known to be related to Alzheimer’s disease. Their aggregation is enhanced at hydrophilic–hydrophobic interfaces, such as a cell membrane surface and air-water interface, and is inhibited by polyphenols, such as myricetin and rosmarinic acid. We review molecular dynamics (MD) simulation approaches of a full-length Aβ peptide, Aβ40, and Aβ(16–22) fragments in these environments. Since these peptides have both hydrophilic and hydrophobic amino acid residues, they tend to exist at the interfaces. The high concentration of the peptides accelerates the aggregation there. In addition, Aβ40 forms a β-hairpin structure, and this structure accelerates the aggregation. We also describe the inhibition mechanism of the Aβ(16–22) aggregation by polyphenols. The aggregation of Aβ(16–22) fragments is caused mainly by the electrostatic attraction between charged amino acid residues known as Lys16 and Glu22. Since polyphenols form hydrogen bonds between their hydroxy and carboxyl groups and these charged amino acid residues, they inhibit the aggregation.

Refined metadynamics through canonical sampling using time-invariant bias potential: A study of polyalcohol dehydration in hot acidic solutions

We propose a canonical sampling method to refine metadynamics simulations a posteriori, where the hills obtained from metadynamics are used as a time-invariant bias potential. In this way, the statistical error in the computed reaction barriers is reduced by an efficient sampling of the collective variable space at the free energy level of interest. This simple approach could be useful particularly when two or more free energy barriers are to be compared among chemical reactions in different or competing conditions. The method was then applied to study the acid dependence of polyalcohol dehydration reactions in high-temperature aqueous solutions. It was found that the reaction proceeds consistently via an S_N 2 mechanism, whereby the free energy of protonation of the hydroxyl group created as an intermediate is affected significantly by the acidic species. Although demonstration is shown for a specific problem, the computational method suggested herein could be generally used for simulations of complex reactions in the condensed phase.

Efficient Conformational Sampling of Collective Motions of Proteins with Principal Component Analysis-Based Parallel Cascade Selection Molecular Dynamics

Molecular dynamics (MD) simulation has become a powerful tool because it provides a time series of protein dynamics at high temporal-spatial resolution. However, the accessible timescales of MD simulation are shorter than those of the biologically rare events. Generally, long-time MD simulations over microseconds are required to detect the rare events. Therefore, it is desirable to develop rare-event-sampling methods. For a rare-event-sampling method, we have developed parallel cascade selection MD (PaCS-MD). PaCS-MD generates transition pathways from a given source structure to a target structure by repeating short-time MD simulations. The key point in PaCS-MD is how to select reasonable candidates (protein configurations) with high potentials to make transitions toward the target structure. In the present study, based on principal component analysis (PCA), we propose PCA-based PaCS-MD to detect rare events of collective motions of a given protein. Here, the PCA-based PaCS-MD is composed of the following two steps. At first, as a preliminary run, PCA is performed using an MD trajectory from the target structure to define a principal coordinate (PC) subspace for describing the collective motions of interest. PCA provides principal modes as eigenvectors to project a protein configuration onto the PC subspace. Then, as a production run, all the snapshots of short-time MD simulations are ranked by inner products (IPs), where an IP is defined between a snapshot and the target structure. Then, snapshots with higher values of the IP are selected as reasonable candidates, and short-time MD simulations are independently restarted from them. By referring to the values of the IP, the PCA-based PaCS-MD repeats the short-time MD simulations from the reasonable candidates that are highly correlated with the target structure. As a demonstration, we applied the PCA-based PaCS-MD to adenylate kinase and detected its large-amplitude (open-closed) transition with a nanosecond-order computational cost.

Energetics and kinetics of substrate analog-coupled staphylococcal nuclease folding revealed by a statistical mechanical approach

Protein conformational changes associated with ligand binding, especially those involving intrinsically disordered proteins, are mediated by tightly coupled intra- and intermolecular events. Such reactions are often discussed in terms of two limiting kinetic mechanisms, conformational selection (CS), where folding precedes binding, and induced fit (IF), where binding precedes folding. It has been shown that coupled folding/binding reactions can proceed along both CS and IF pathways with the flux ratio depending on conditions such as ligand concentration. However, the structural and energetic basis of such complex reactions remains poorly understood. Therefore, we used experimental, theoretical, and computational approaches to explore structural and energetic aspects of the coupled-folding/binding reaction of staphylococcal nuclease in the presence of the substrate analog adenosine-3',5'-diphosphate. Optically monitored equilibrium and kinetic data, combined with a statistical mechanical model, gave deeper insight into the relative importance of specific and Coulombic protein-ligand interactions in governing the reaction mechanism. We also investigated structural aspects of the reaction at the residue level using NMR and all-atom replica-permutation molecular dynamics simulations. Both approaches yielded clear evidence for accumulation of a transient protein-ligand encounter complex early in the reaction under IF-dominant conditions. Quantitative analysis of the equilibrium/kinetic folding revealed that the ligand-dependent CS-to-IF shift resulted from stabilization of the compact transition state primarily by weakly ligand-dependent Coulombic interactions with smaller contributions from specific binding energies. At a more macroscopic level, the CS-to-IF shift was represented as a displacement of the reaction "route" on the free energy surface, which was consistent with a flux analysis.

Efficient Irreversible Monte Carlo Samplers

We present here two irreversible Markov chain Monte Carlo algorithms for general discrete state systems. One of the algorithms is based on the random-scan Gibbs sampler for discrete states and the other on its improved version, the Metropolized-Gibbs sampler. The algorithms we present incorporate the lifting framework with skewed detailed balance condition and construct irreversible Markov chains that satisfy the balance condition. We have applied our algorithms to 1D 4-state Potts model. The integrated autocorrelation times for magnetization and energy density indicate a reduction of the dynamical scaling exponent from z ≈ 1 to z ≈ 1/2. In addition, we have generalized an irreversible Metropolis-Hastings algorithm with skewed detailed balance, initially introduced by Turitsyn et al. [ Physica D 2011, 240, 410] for the mean field Ising model, to be now readily applicable to classical spin systems in general; application to 1D 4-state Potts model indicate a square root reduction of the mixing time at high temperatures.

Biophysical research in Okazaki, Japan

This commentary summarizes the recent biophysical research conducted at the National Institute for Basic Biology, the National Institute for Physiological Sciences, and the Institute for Molecular Science in Okazaki, Japan.

Nontargeted Parallel Cascade Selection Molecular Dynamics Based on a Nonredundant Selection Rule for Initial Structures Enhances Conformational Sampling of Proteins

Nontargeted parallel cascade selection molecular dynamics (nt-PaCS-MD) is a method for enhanced conformational sampling of proteins. To search a broad conformational subspace, nt-PaCS-MD repeats cycles of conformational resampling from relevant initial structures. Generally, the conformational sampling efficiency of nt-PaCS-MD depends on a selection rule for the initial structures. In the original nt-PaCS-MD, the initial structures were selected by referring to structural distributions of protein configurations generated by conformational resampling (multiple short-time MD simulations). However, their structural redundancy among the initial structures was neglected for the cycles of conformational resampling, indicating that similar protein configurations might be frequently specified and resampled in every cycle in the original nt-PaCS-MD. To reduce the possibility of resampling from redundant initial structures, we propose an alternative selection rule that accounts for structural similarity among the initial structures. Specifically, a pairwise root-mean-square deviation (RMSD) is defined for all of the initial structures selected for all of the past cycles. Then a set of protein configurations with a larger pairwise RMSD is sequentially specified and resampled in the next cycle, which is regarded to as a history-dependent selection of initial structures by considering a profile of the past specified initial structures. The present scheme, termed extended nt-PaCS-MD, prevents us from resampling a set of redundant protein configurations. To check the conformational sampling efficiency of the extended nt-PaCS-MD, we used a middle-sized protein, T4 lysozyme, in explicit water. Through the assessment, this extended nt-PaCS-MD identified the open-closed transitions of T4 lysozyme more efficiently than the original nt-PaCS-MD.

Replica sub-permutation method for molecular dynamics and monte carlo simulations

We propose an improvement of the replica-exchange and replica-permutation methods, which we call the replica sub-permutation method (RSPM). Instead of considering all permutations, this method uses a new algorithm referred to as sub-permutation to perform parameter transition. The RSPM succeeds in reducing the number of combinations between replicas and parameters without the loss of sampling efficiency. For comparison, we applied the replica sub-permutation, replica-permutation, and replica-exchange methods to a β-hairpin mini protein, chignolin, in explicit water. We calculated the transition ratio and number of tunneling events in the parameter space, the number of folding-unfolding events, the autocorrelation function, and the autocorrelation time as measures of sampling efficiency. The results indicate that among the three methods, the proposed RSPM is the most efficient in both parameter and conformational spaces. © 2019 Wiley Periodicals, Inc.

Molecular simulations by generalized-ensemble algorithms in isothermal-isobaric ensemble

Generalized-ensemble algorithms are powerful techniques for investigating biomolecules such as protein, DNA, lipid membrane, and glycan. The generalized-ensemble algorithms were originally developed in the canonical ensemble. On the other hand, not only temperature but also pressure is controlled in experiments. Additionally, pressure is used as perturbation to study relationship between function and structure of biomolecules. For this reason, it is important to perform efficient conformation sampling based on the isothermal-isobaric ensemble. In this article, we review a series of the generalized-ensemble algorithms in the isothermal-isobaric ensemble: multibaric-multithermal, pressure- and temperature-simulated tempering, replica-exchange, and replica-permutation methods. These methods achieve more efficient simulation than the conventional isothermal-isobaric simulation. Furthermore, the isothermal-isobaric generalized-ensemble simulation samples conformations of biomolecules from wider range of temperature and pressure. Thus, we can estimate physical quantities more accurately at any temperature and pressure values. The applications to the biomolecular system are also presented.

Theoretical analysis on thermodynamic stability of chignolin

Understanding the dominant factor in thermodynamic stability of proteins remains an open challenge. Kauzmann's hydrophobic interaction hypothesis, which considers hydrophobic interactions between nonpolar groups as the dominant factor, has been widely accepted for about sixty years and attracted many scientists. The hypothesis, however, has not been verified or disproved because it is difficult, both theoretically and experimentally, to quantify the solvent effects on the free energy change in protein folding. Here, we developed a computational method for extracting the dominant factor behind thermodynamic stability of proteins and applied it to a small, designed protein, chignolin. The resulting free energy profile quantitatively agreed with the molecular dynamics simulations. Decomposition of the free energy profile indicated that intramolecular interactions predominantly stabilized collapsed conformations, whereas solvent-induced interactions, including hydrophobic ones, destabilized them. These results obtained for chignolin were consistent with the site-directed mutagenesis and calorimetry experiments for globular proteins with hydrophobic interior cores.

Alchemical Free-Energy Calculations by Multiple-Replica λ-Dynamics: The Conveyor Belt Thermodynamic Integration Scheme

A new method is proposed to calculate alchemical free-energy differences based on molecular dynamics (MD) simulations, called the conveyor belt thermodynamic integration (CBTI) scheme. As in thermodynamic integration (TI), K replicas of the system are simulated at different values of the alchemical coupling parameter λ. The number K is taken to be even, and the replicas are equally spaced on a forward-turn-backward-turn path, akin to a conveyor belt (CB) between the two physical end-states; and as in λ-dynamics (λD), the λ-values associated with the individual systems evolve in time along the simulation. However, they do so in a concerted fashion, determined by the evolution of a single dynamical variable Λ of period 2π controlling the advance of the entire CB. Thus, a change of Λ is always associated with K/2 equispaced replicas moving forward and K/2 equispaced replicas moving backward along λ. As a result, the effective free-energy profile of the replica system along Λ is periodic of period 2 πK^-1, and the magnitude of its variations decreases rapidly upon increasing K, at least as K^-1 in the limit of large K. When a sufficient number of replicas is used, these variations become small, which enables a complete and quasi-homogeneous coverage of the λ-range by the replica system, without application of any biasing potential. If desired, a memory-based biasing potential can still be added to further homogenize the sampling, the preoptimization of which is computationally inexpensive. The final free-energy profile along λ is calculated similarly to TI, by binning of the Hamiltonian λ-derivative as a function of λ considering all replicas simultaneously, followed by quadrature integration. The associated quadrature error can be kept very low owing to the continuous and quasi-homogeneous λ-sampling. The CBTI scheme can be viewed as a continuous/deterministic/dynamical analog of the Hamiltonian replica-exchange/permutation (HRE/HRP) schemes or as a correlated multiple-replica analog of the λD or λ-local elevation umbrella sampling (λ-LEUS) schemes. Compared to TI, it shares the advantage of the latter schemes in terms of enhanced orthogonal sampling, i.e. the availability of variable-λ paths to circumvent conformational barriers present at specific λ-values. Compared to HRE/HRP, it permits a deterministic and continuous sampling of the λ-range, is expected to be less sensitive to possible artifacts of the thermo- and barostating schemes, and bypasses the need to carefully preselect a λ-ladder and a swapping-attempt frequency. Compared to λ-LEUS, it eliminates (or drastically reduces) the dead time associated with the preoptimization of a biasing potential. The goal of this article is to provide the mathematical/physical formulation of the proposed CBTI scheme, along with an initial application of the method to the calculation of the hydration free energy of methanol.

Direct coupling of first-principles calculations with replica exchange Monte Carlo sampling of ion disorder in solids

We demonstrate the feasibility of performing sufficient configurational sampling of disordered oxides directly from first-principles without resorting to the use of fitted models such as cluster expansion. This is achieved by harnessing the power of modern-day cluster supercomputers using the replica exchange Monte Carlo method coupled directly with structural relaxation and energy calculation performed by density functional codes. The idea is applied successfully to the calculation of the temperature-dependence of the degree of inversion in the cation sublattice of MgAl₂O₄ spinel oxide. The possibility of bypassing fitting models will lead to investigation of disordered systems where cluster expansion is known to perform badly, for example, systems with large lattice deformation due to defects, or systems where long-range interactions dominate such as electrochemical interfaces.

Replica-Exchange Methods for Biomolecular Simulations

In this study, a replica-exchange method was developed to overcome conformational sampling difficulties in computer simulations of spin glass or other systems with rugged free-energy landscapes. This method was then applied to the protein-folding problem in combination with molecular dynamics (MD) simulation. Owing to its simplicity and sampling efficiency, the replica-exchange method has been applied to many other biological problems and has been continuously improved. The method has often been combined with other sampling techniques, such as umbrella sampling, free-energy perturbation, metadynamics, and Gaussian accelerated MD (GaMD). In this chapter, we first summarize the original replica-exchange molecular dynamics (REMD) method and discuss how new algorithms related to the original method are implemented to add new features. Heterogeneous and flexible structures of an N-glycan in a solution are simulated as an example of applications by REMD, replica exchange with solute tempering, and GaMD. The sampling efficiency of these methods on the N-glycan system and the convergence of the free-energy changes are compared. REMD simulation protocols and trajectory analysis using the GENESIS software are provided to facilitate the practical use of advanced simulation methods.

Development of isothermal-isobaric replica-permutation method for molecular dynamics and Monte Carlo simulations and its application to reveal temperature and pressure dependence of folded, misfolded, and unfolded states of chignolin

We developed a two-dimensional replica-permutation molecular dynamics method in the isothermal-isobaric ensemble. The replica-permutation method is a better alternative to the replica-exchange method. It was originally developed in the canonical ensemble. This method employs the Suwa-Todo algorithm, instead of the Metropolis algorithm, to perform permutations of temperatures and pressures among more than two replicas so that the rejection ratio can be minimized. We showed that the isothermal-isobaric replica-permutation method performs better sampling efficiency than the isothermal-isobaric replica-exchange method and infinite swapping method. We applied this method to a β-hairpin mini protein, chignolin. In this simulation, we observed not only the folded state but also the misfolded state. We calculated the temperature and pressure dependence of the fractions on the folded, misfolded, and unfolded states. Differences in partial molar enthalpy, internal energy, entropy, partial molar volume, and heat capacity were also determined and agreed well with experimental data. We observed a new phenomenon that misfolded chignolin becomes more stable under high-pressure conditions. We also revealed this mechanism of the stability as follows: TYR2 and TRP9 side chains cover the hydrogen bonds that form a β-hairpin structure. The hydrogen bonds are protected from the water molecules that approach the protein as the pressure increases.

On-the-Fly Specifications of Reaction Coordinates in Parallel Cascade Selection Molecular Dynamics Accelerate Conformational Transitions of Proteins

Parallel Cascade Selection Molecular Dynamics (PaCS-MD) is an efficient conformational sampling method for generating a set of reactive trajectories that connect a given reactant and a product. In PaCS-MD, initial structures relevant to conformational transitions are reasonably selected by referring to a set of reaction coordinates (RCs), and short-time molecular dynamics (MD) simulations are independently launched from them. To efficiently perform PaCS-MD, specifications of RCs are essential, but specifying reasonable RCs is generally nontrivial. In the present study, we propose on-the-fly specifications of RCs as an extended PaCS-MD. In the present method, n types of RCs are provided as candidates a priori as follows: RC = (X₁, X₂, ..., X _n), and one of the RCs is specified in a cycle-dependent manner, i.e. the reasonable RC is searched at every cycle by evaluating gradients of the RCs, i.e. RC with the steepest gradient for cycle is regarded as the reasonable RC, and conformational resampling proceeds along it, promoting conformational transition of a given protein. For a demonstration, the extended PaCS-MD was applied to reproduce the open-closed conformational transition of T4 lysozyme (T4L). As candidates of possible RCs, (1) root-mean square distance, (2) principal coordinates, (3) accessible surface area, (4) radius of gyration, and (5) end-to-end distance were adopted in the cycle-dependent specifications of RCs. Through the demonstration, the extended PaCS-MD successfully reproduced the conformational transition from the open to closed states of T4L. As a more complicated practice, a dimerization process of diubiquitin was efficiently reproduced with the extended PaCS-MD, showing the high conformational sampling efficiency of the present algorithm. In contrast, the conventional PaCS-MD with a fixed RC sometimes failed to generate a set of reactive trajectories when an unreasonable RC was specified, i.e. the conformational sampling efficiency of PaCS-MD might more or less depend on the specified RCs. Judging from the present demonstrations, on-the-fly specifications of RCs might be effective in reproducing/predicting essential transitions of a given protein.

Self-Avoiding Conformational Sampling Based on Histories of Past Conformational Searches

Self-avoiding conformational sampling (SACS) is proposed as an enhanced conformational sampling method for proteins. In SACS, the following conformational resampling is repeated for a given protein: (1) identification of newly visited states in a subspace and (2) conformational resampling by restarting short-time molecular dynamics (MD) simulations from the newly visited states. To identify the newly visited states, a set of history-dependent histograms projected onto the subspace is used. One is constructed from the trajectories sampled at the current (ith) cycle, and the other is constructed from all of the trajectories accumulated up through the previous ((i - 1)th) cycle. By reference to the history-dependent histograms, the newly visited states appearing at the current (ith) cycle are defined as a difference set between them. By repeating the cycle of conformational resampling, SACS prevents the system from revisiting states that have already been visited for previous cycles, promoting structural transitions via resampling from the newly visited states. To verify the conformational sampling efficiency of SACS, the present method was applied to reveal underlying mechanisms of biologically important domain motions of maltodextrin binding protein in explicit water and successfully reproduced the open-closed transition with a reasonable (nanosecond-order) computational cost.

Efficacy of independence sampling in replica exchange simulations of ordered and disordered proteins

Recasting temperature replica exchange (T-RE) as a special case of Gibbs sampling has led to a simple and efficient scheme for enhanced mixing (Chodera and Shirts, J. Chem. Phys., 2011, 135, 194110). To critically examine if T-RE with independence sampling (T-REis) improves conformational sampling, we performed T-RE and T-REis simulations of ordered and disordered proteins using coarse-grained and atomistic models. The results demonstrate that T-REis effectively increase the replica mobility in temperatures space with minimal computational overhead, especially for folded proteins. However, enhanced mixing does not translate well into improved conformational sampling. The convergences of thermodynamic properties interested are similar, with slight improvements for T-REis of ordered systems. The study re-affirms the efficiency of T-RE does not appear to be limited by temperature diffusion, but by the inherent rates of spontaneous large-scale conformational re-arrangements. Due to its simplicity and efficacy of enhanced mixing, T-REis is expected to be more effective when incorporated with various Hamiltonian-RE protocols. © 2017 Wiley Periodicals, Inc.

Theoretical approaches for dynamical ordering of biomolecular systems

BACKGROUND

Living systems are characterized by the dynamic assembly and disassembly of biomolecules. The dynamical ordering mechanism of these biomolecules has been investigated both experimentally and theoretically. The main theoretical approaches include quantum mechanical (QM) calculation, all-atom (AA) modeling, and coarse-grained (CG) modeling. The selected approach depends on the size of the target system (which differs among electrons, atoms, molecules, and molecular assemblies). These hierarchal approaches can be combined with molecular dynamics (MD) simulation and/or integral equation theories for liquids, which cover all size hierarchies.

SCOPE OF REVIEW

We review the framework of quantum mechanical/molecular mechanical (QM/MM) calculations, AA MD simulations, CG modeling, and integral equation theories. Applications of these methods to the dynamical ordering of biomolecular systems are also exemplified.

MAJOR CONCLUSIONS

The QM/MM calculation enables the study of chemical reactions. The AA MD simulation, which omits the QM calculation, can follow longer time-scale phenomena. By reducing the number of degrees of freedom and the computational cost, CG modeling can follow much longer time-scale phenomena than AA modeling. Integral equation theories for liquids elucidate the liquid structure, for example, whether the liquid follows a radial distribution function.

GENERAL SIGNIFICANCE

These theoretical approaches can analyze the dynamic behaviors of biomolecular systems. They also provide useful tools for exploring the dynamic ordering systems of biomolecules, such as self-assembly. This article is part of a Special Issue entitled "Biophysical Exploration of Dynamical Ordering of Biomolecular Systems" edited by Dr. Koichi Kato.

Temperature-shuffled parallel cascade selection molecular dynamics accelerates the structural transitions of proteins

Parallel cascade selection molecular dynamics (PaCS-MD) is an enhanced conformational sampling method for searching structural transition pathways from a given reactant to a product. Recently, a temperature-aided PaCS-MD (Vinod et al., Eur. Biophys. J. 2016, 45, 463) has been proposed as its extension, in which the temperatures were introduced as additional parameters in conformational resampling, whereas the temperature is fixed in the original PaCS-MD. In the present study, temperature-shuffled PaCS-MD is proposed as a further extension of temperature-aided PaCS-MD in which the temperatures are shuffled among different replicas at the beginning of each cycle of conformational resampling. To evaluate their conformational sampling efficiencies, the original, temperature-aided, and temperature-shuffled PaCS-MD were applied to a protein-folding process of Trp-cage, and their minimum computational costs to identify the native state were addressed. Through the evaluation, it was confirmed that temperature-shuffled PaCS-MD remarkably accelerated the protein-folding process of Trp-cage compared with the other methods. © 2017 Wiley Periodicals, Inc.

Enhanced conformational sampling to visualize a free-energy landscape of protein complex formation

We introduce various, recently developed, generalized ensemble methods, which are useful to sample various molecular configurations emerging in the process of protein-protein or protein-ligand binding. The methods introduced here are those that have been or will be applied to biomolecular binding, where the biomolecules are treated as flexible molecules expressed by an all-atom model in an explicit solvent. Sampling produces an ensemble of conformations (snapshots) that are thermodynamically probable at room temperature. Then, projection of those conformations to an abstract low-dimensional space generates a free-energy landscape. As an example, we show a landscape of homo-dimer formation of an endothelin-1-like molecule computed using a generalized ensemble method. The lowest free-energy cluster at room temperature coincided precisely with the experimentally determined complex structure. Two minor clusters were also found in the landscape, which were largely different from the native complex form. Although those clusters were isolated at room temperature, with rising temperature a pathway emerged linking the lowest and second-lowest free-energy clusters, and a further temperature increment connected all the clusters. This exemplifies that the generalized ensemble method is a powerful tool for computing the free-energy landscape, by which one can discuss the thermodynamic stability of clusters and the temperature dependence of the cluster networks.

Oligomer Formation of Amyloid-β(29-42) from Its Monomers Using the Hamiltonian Replica-Permutation Molecular Dynamics Simulation

Oligomers of amyloid-β peptides (Aβ) are formed during the early stage of the amyloidogenesis process and exhibit neurotoxicity. The oligomer formation process of Aβ and even that of Aβ fragments are still poorly understood, though understanding of these processes is essential for remedying Alzheimer's disease. In order to better understand the oligomerization process of the C-terminal Aβ fragment Aβ(29-42) at the atomic level, we performed the Hamiltonian replica-permutation molecular dynamics simulation with Aβ(29-42) molecules using the explicit water solvent model. We observed that oligomers increased in size through the sequential addition of monomers to the oligomer, rather than through the assembly of small oligomers. Moreover, solvent effects played an important role in this oligomerization process.

Multistate λ-local-elevation umbrella-sampling (MS-λ-LEUS): method and application to the complexation of cations by crown ethers

An extension of the λ-local-elevation umbrella-sampling (λ-LEUS) scheme [ Bieler et al. J. Chem. Theory Comput. 2014 , 10 , 3006 ] is proposed to handle the multistate (MS) situation, i.e. the calculation of the relative free energies of multiple physical states based on a single simulation. The key element of the MS-λ-LEUS approach is to use a single coupling variable Λ controlling successive pairwise mutations between the states of interest in a cyclic fashion. The Λ variable is propagated dynamically as an extended-system variable, using a coordinate transformation with plateaus and a memory-based biasing potential as in λ-LEUS. Compared to other available MS schemes (one-step perturbation, enveloping distribution sampling and conventional λ-dynamics) the proposed method presents a number of important advantages, namely: (i) the physical states are visited explicitly and over finite time periods; (ii) the extent of unphysical space required to ensure transitions is kept minimal and, in particular, one-dimensional; (iii) the setup protocol solely requires the topologies of the physical states; and (iv) the method only requires limited modifications in a simulation code capable of handling two-state mutations. As an initial application, the absolute binding free energies of five alkali cations to three crown ethers in three different solvents are calculated. The results are found to reproduce qualitatively the main experimental trends and, in particular, the experimental selectivity of 18C6 for K(+) in water and methanol, which is interpreted in terms of opposing trends along the cation series between the solvation free energy of the cation and the direct electrostatic interactions within the complex.

Characterization of the three-dimensional free energy manifold for the uracil ribonucleoside from asynchronous replica exchange simulations

Replica exchange molecular dynamics has emerged as a powerful tool for efficiently sampling free energy landscapes for conformational and chemical transitions. However, daunting challenges remain in efficiently getting such simulations to scale to the very large number of replicas required to address problems in state spaces beyond two dimensions. The development of enabling technology to carry out such simulations is in its infancy, and thus it remains an open question as to which applications demand extension into higher dimensions. In the present work, we explore this problem space by applying asynchronous Hamiltonian replica exchange molecular dynamics with a combined quantum mechanical/molecular mechanical potential to explore the conformational space for a simple ribonucleoside. This is done using a newly developed software framework capable of executing >3,000 replicas with only enough resources to run 2,000 simultaneously. This may not be possible with traditional synchronous replica exchange approaches. Our results demonstrate 1.) the necessity of high dimensional sampling simulations for biological systems, even as simple as a single ribonucleoside, and 2.) the utility of asynchronous exchange protocols in managing simultaneous resource requirements expected in high dimensional sampling simulations. It is expected that more complicated systems will only increase in computational demand and complexity, and thus the reported asynchronous approach may be increasingly beneficial in order to make such applications available to a broad range of computational scientists.