Ensuring Mixing Efficiency of Replica-Exchange Molecular Dynamics Simulations

Alchemical Enhanced Sampling with Optimized Phase Space Overlap

An alchemical enhanced sampling (ACES) method has recently been introduced to facilitate importance sampling in free energy simulations. The method achieves enhanced sampling from Hamiltonian replica exchange within a dual topology framework while utilizing new smoothstep softcore potentials. A common sampling problem encountered in lead optimization is the functionalization of aromatic rings that exhibit distinct conformational preferences when interacting with the protein. It is difficult to converge the distribution of ring conformations due to the long time scale of ring flipping events; however, the ACES method addresses this issue by modeling the syn and anti ring conformations within a dual topology. ACES thereby samples the conformer distributions by alchemically tunneling between states, as opposed to traversing a physical pathway with a high rotational barrier. We demonstrate the use of ACES to overcome conformational sampling issues involving ring flipping in ML300-derived noncovalent inhibitors of SARS-CoV-2 Main Protease (Mpro). The demonstrations explore how the use of replica exchange and the choice of softcore selection affects the convergence of the ring conformation distributions. Furthermore, we examine how the accuracy of the calculated free energies is affected by the degree of phase space overlap (PSO) between adjacent states (i.e., between neighboring λ-windows) and the Hamiltonian replica exchange acceptance ratios. Both of these factors are sensitive to the spacing between the intermediate states. We introduce a new method for choosing a schedule of λ values. The method analyzes short "burn-in" simulations to construct a 2D map of the nonlocal PSO. The schedule is obtained by optimizing an alchemical pathway on the 2D map that equalizes the PSO between the λ intervals. The optimized phase space overlap λ-spacing method (Opt-PSO) leads to more numerous end-to-end single passes and round trips due to the correlation between PSO and Hamiltonian replica exchange acceptance ratios. The improved exchange statistics enhance the efficiency of ACES method. The method has been implemented into the FE-ToolKit software package, which is freely available.

Q-RepEx: A Python pipeline to increase the sampling of empirical valence bond simulations

The exploration of chemical systems occurs on complex energy landscapes. Comprehensively sampling rugged energy landscapes with many local minima is a common problem for molecular dynamics simulations. These multiple local minima trap the dynamic system, preventing efficient sampling. This is a particular challenge for large biochemical systems with many degrees of freedom. Replica exchange molecular dynamics (REMD) is an approach that accelerates the exploration of the conformational space of a system, and thus can be used to enhance the sampling of complex biomolecular processes. In parallel, the empirical valence bond (EVB) approach is a powerful approach for modeling chemical reactivity in biomolecular systems. Here, we present an open-source Python-based tool that interfaces with the Q simulation package, and increases the sampling efficiency of the EVB free energy perturbation/umbrella sampling approach by means of REMD. This approach, Q-RepEx, both decreases the computational cost of the associated REMD-EVB simulations, and opens the door to more efficient studies of biochemical reactivity in systems with significant conformational fluctuations along the chemical reaction coordinate.

Skipping the Replica Exchange Ladder with Normalizing Flows

We combine replica exchange (parallel tempering) with normalizing flows, a class of deep generative models. These two sampling strategies complement each other, resulting in an efficient method for sampling molecular systems characterized by rare events, which we call learned replica exchange (LREX). In LREX, a normalizing flow is trained to map the configurations of the fastest-mixing replica into configurations belonging to the target distribution, allowing direct exchanges between the two without the need to simulate intermediate replicas. This can significantly reduce the computational cost compared to standard replica exchange. The proposed method also offers several advantages with respect to Boltzmann generators that directly use normalizing flows to sample the target distribution. We apply LREX to some prototypical molecular dynamics systems, highlighting the improvements over previous methods.

Using a Coarse-Grained Modeling Framework to Identify Oligomeric Motifs with Tunable Secondary Structure

Coarse-grained modeling can be used to explore general theories that are independent of specific chemical detail. In this paper, we present cg_openmm, a Python-based simulation framework for modeling coarse-grained hetero-oligomers and screening them for structural and thermodynamic characteristics of cooperative secondary structures. cg_openmm facilitates the building of coarse-grained topology and random starting configurations, setup of GPU-accelerated replica exchange molecular dynamics simulations with the OpenMM software package, and features a suite of postprocessing thermodynamic and structural analysis tools. In particular, native contact analysis, heat capacity calculations, and free energy of folding calculations are used to identify and characterize cooperative folding transitions and stable secondary structures. In this work, we demonstrate the capabilities of cg_openmm on a simple 1-1 Lennard-Jones coarse-grained model, in which each residue contains 1 backbone and 1 side-chain bead. By scanning both nonbonded and bonded force-field parameter spaces at the coarse-grained level, we identify and characterize sets of parameters which result in the formation of stable helices through cooperative folding transitions. Moreover, we show that the geometries and stabilities of these helices can be tuned by manipulating the force-field parameters.

Molecular dynamics simulations of bacterial outer membrane lipid extraction: Adequate sampling?

The outer membrane of Gram-negative bacteria is almost exclusively composed of lipopolysaccharide in its outer leaflet, whereas the inner leaflet contains a mixture of phospholipids. Lipopolysaccharide diffuses at least an order of magnitude slower than phospholipids, which can cause issues for molecular dynamics simulations in terms of adequate sampling. Here, we test a number of simulation protocols for their ability to achieve convergence with reasonable computational effort using the MARTINI coarse-grained force-field. This is tested in the context both of potential of mean force (PMF) calculations for lipid extraction from membranes and of lateral mixing within the membrane phase. We find that decoupling the cations that cross-link the lipopolysaccharide headgroups from the extracted lipid during PMF calculations is the best approach to achieve convergence comparable to that for phospholipid extraction. We also show that lateral lipopolysaccharide mixing/sorting is very slow and not readily addressable even with Hamiltonian replica exchange. We discuss why more sorting may be unrealistic for the short (microseconds) timescales we simulate and provide an outlook for future studies of lipopolysaccharide-containing membranes.

An Implementation of Replica Exchange with Dynamical Scaling for Efficient Large-Scale Simulations

An implementation of the replica exchange with dynamical scaling (REDS) method in the commonly used molecular dynamics program GROMACS is presented. REDS is a replica exchange method that requires fewer replicas than conventional replica exchange while still providing data over a range of temperatures and can be used in either constant volume or constant pressure ensembles. Details for running REDS simulations are given, and an application to the human islet amyloid polypeptide (hIAPP) 11-25 fragment shows that the model efficiently samples conformational space.

Simulated tempering with irreversible Gibbs sampling techniques

We present here two novel algorithms for simulated tempering simulations, which break the detailed balance condition (DBC) but satisfy the skewed detailed balance to ensure invariance of the target distribution. The irreversible methods we present here are based on Gibbs sampling and concern breaking DBC at the update scheme of the temperature swaps. We utilize three systems as a test bed for our methods: a Markov chain Monte Carlo simulation on a simple system described by a one-dimensional double well potential, the Ising model, and molecular dynamics simulations on alanine pentapeptide (ALA5). The relaxation times of inverse temperature, magnetic susceptibility, and energy density for the Ising model indicate clear gains in sampling efficiency over conventional Gibbs sampling techniques with DBC and also over the conventionally used simulated tempering with the Metropolis-Hastings (MH) scheme. Simulations on ALA5 with a large number of temperatures indicate distinct gains in mixing times for inverse temperature and consequently the energy of the system compared to conventional MH. With no additional computational overhead, our methods were found to be more efficient alternatives to the conventionally used simulated tempering methods with DBC. Our algorithms should be particularly advantageous in simulations of large systems with many temperature ladders, as our algorithms showed a more favorable constant scaling in Ising spin systems as compared with both reversible and irreversible MH algorithms. In future applications, our irreversible methods can also be easily tailored to utilize a given dynamical variable other than temperature to flatten rugged free energy landscapes.

myPresto/omegagene 2020: a molecular dynamics simulation engine for virtual-system coupled sampling

The molecular dynamics (MD) method is a promising approach for investigating the molecular mechanisms of microscopic phenomena. In particular, generalized ensemble MD methods can efficiently explore the conformational space with a rugged free-energy surface. However, the implementation and acquisition of technical knowledge for each generalized ensemble MD method are not straightforward for end-users. Here, we present a new version of the myPresto/omegagene software, which is an MD simulation engine tailored for a series of generalized ensemble methods, which are virtual-system coupled multicanonical MD (V-McMD), virtual-system coupled adaptive umbrella sampling (V-AUS), and virtual-system coupled canonical MD (VcMD). This program has been applied in several studies analyzing free-energy landscapes of a variety of molecular systems with all-atom simulations. The updated version provides new functionality for coarse-grained simulations powered by the hydrophobicity scale method. The software package includes a step-by-step tutorial document for enhanced conformational sampling of the poly-glutamine (poly-Q) oligomer expressed as a one-bead per residue model. The myPresto/omegagene software is freely available at the following URL: https://github.com/kotakasahara/omegagene under the Apache2 license.

A linker of the proline-threonine repeating motif sequence is bimodal

The linker of the endoglucanase from Xanthomonas campestris pv. campestris ((PT)₁₂) has a specific sequence, a repeating proline-threonine motif. In order to understand its role, it has been compared to a regular sequence linker, in this work-the cellobiohydrolase 2 from Trichoderma reesei (CBH2). Elastic properties of the two linkers have been estimated by calculating free energy profile along the linker length from an enhanced sampling molecular dynamics simulation. The (PT)₁₂ exhibits more pronounced elastic behaviour than CBH2. The PT repeating motif results in a two-mode energy profile which could be very useful in the enzyme motions along the substrate during hydrolytic catalysis.

Studies on Molecular Dynamics of Intrinsically Disordered Proteins and Their Fuzzy Complexes: A Mini-Review

The molecular dynamics (MD) method is a promising approach toward elucidating the molecular mechanisms of intrinsically disordered regions (IDRs) of proteins and their fuzzy complexes. This mini-review introduces recent studies that apply MD simulations to investigate the molecular recognition of IDRs. Firstly, methodological issues by which MD simulations treat IDRs, such as developing force fields, treating periodic boundary conditions, and enhanced sampling approaches, are discussed. Then, several examples of the applications of MD to investigate molecular interactions of IDRs in terms of the two kinds of complex formations; coupled-folding and binding and fuzzy complex. MD simulations provide insight into the molecular mechanisms of these binding processes by sampling conformational ensembles of flexible IDRs. In particular, we focused on all-atom explicit-solvent MD simulations except for studies of higher-order assembly of IDRs. Recent advances in MD methods, and computational power make it possible to dissect the molecular details of realistic molecular systems involving the dynamic behavior of IDRs.

Massive-Scale Binding Free Energy Simulations of HIV Integrase Complexes Using Asynchronous Replica Exchange Framework Implemented on the IBM WCG Distributed Network

To perform massive-scale replica exchange molecular dynamics (REMD) simulations for calculating binding free energies of protein-ligand complexes, we implemented the asynchronous replica exchange (AsyncRE) framework of the binding energy distribution analysis method (BEDAM) in implicit solvent on the IBM World Community Grid (WCG) and optimized the simulation parameters to reduce the overhead and improve the prediction power of the WCG AsyncRE simulations. We also performed the first massive-scale binding free energy calculations using the WCG distributed computing grid and 301 ligands from the SAMPL4 challenge for large-scale binding free energy predictions of HIV-1 integrase complexes. In total there are ∼10000 simulated complexes, ∼1 million replicas, and ∼2000 μs of aggregated MD simulations. Running AsyncRE MD simulations on the WCG requires accepting a trade-off between the number of replicas that can be run (breadth) and the number of full RE cycles that can be completed per replica (depth). As compared with synchronous Replica Exchange (SyncRE) running on tightly coupled clusters like XSEDE, on the WCG many more replicas can be launched simultaneously on heterogeneous distributed hardware, but each full RE cycle requires more overhead. We compared the WCG results with that from AutoDock and more advanced RE simulations including the use of flattening potentials to accelerate sampling of selected degrees of freedom of ligands and/or receptors related to slow dynamics due to high energy barriers. We propose a suitable strategy of RE simulations to refine high throughput docking results which can be matched to corresponding computing resources: from HPC clusters, to small or medium-size distributed campus grids, and finally to massive-scale computing networks including millions of CPUs like the resources available on the WCG.

Best Practices for Quantification of Uncertainty and Sampling Quality in Molecular Simulations [Article v1.0]

The quantitative assessment of uncertainty and sampling quality is essential in molecular simulation. Many systems of interest are highly complex, often at the edge of current computational capabilities. Modelers must therefore analyze and communicate statistical uncertainties so that "consumers" of simulated data understand its significance and limitations. This article covers key analyses appropriate for trajectory data generated by conventional simulation methods such as molecular dynamics and (single Markov chain) Monte Carlo. It also provides guidance for analyzing some 'enhanced' sampling approaches. We do not discuss systematic errors arising, e.g., from inaccuracy in the chosen model or force field.

Influence of various parameters in the replica-exchange molecular dynamics method: Number of replicas, replica-exchange frequency, and thermostat coupling time constant

The replica-exchange molecular dynamics (REMD) method has been used for conformational sampling of various biomolecular systems. To maximize sampling efficiency, some adjustable parameters must be optimized. Although it is agreed that shorter intervals between the replica-exchange attempts enhance traversals in the temperature space, details regarding the artifacts caused by these short intervals are controversial. In this study, we revisit this problem by performing REMD simulations on an alanine octapeptide in an implicit solvent. Fifty different sets of conditions, which are a combination of five replica-exchange periods, five different numbers of replicas, and two thermostat coupling time constants, were investigated. As a result, although short replica-exchange intervals enhanced the traversals in the temperature space, they led to artifacts in the ensemble average of the temperature, potential energy, and helix content. With extremely short replica-exchange intervals, i.e., attempted at every time step, the ensemble average of the temperature deviated from the thermostat temperature by ca. 7 K. Differences in the ensembles were observed even for larger replica-exchange intervals (between 100 and 1,000 steps). In addition, the shorter thermostat coupling time constant reduced the artifacts found when short replica-exchange intervals were used, implying that these artifacts are caused by insufficient thermal relaxation between the replica-exchange events. Our results will be useful to reduce the artifacts found in REMD simulations by adjusting some key parameters.

Aqueous ionic liquids influence the disulfide bond isoform equilibrium in conotoxin AuIB: a consequence of the Hofmeister effect?

The appearance of several disulfide bond isoforms in multiple cysteine containing venom peptides poses a significant challenge in their synthesis and purification under laboratory conditions. Recent experiments suggest that careful tuning of solvent and temperature conditions can propel the disulfide bond isoform equilibrium in favor of the most potent, native form. Certain aqueous ionic liquids (ILs) have proven significantly useful as solvents for this purpose, while exceptions have also been noted. To elucidate the molecular level origin behind such a preference, we report a detailed explicit solvent replica exchange molecular dynamics study of a conotoxin, AuIB, in pure water and four different aqueous IL solutions (~45-60% v/v). The ILs studied here are comprised of cations like 1-ethyl-3-methyl-imidazolium (Im₂₁⁺) or 1-butyl-3-methyl-imidazolium (Im₄₁⁺) coupled with either acetate (OAc^-) or chloride (Cl^-) as the counter anion. Our simulations unfold interesting features of the conformational spaces sampled by the peptide and its solvation in pure water and aqueous IL solutions. Detailed investigation into populations of the globular disulfide bond isoform of AuIB in aqueous IL solutions reveal distinct trends which might be related to the Hofmeister effect of the cation and anion of the IL and of specific interactions of the aqueous IL solutions with the peptide. In accordance with experimental observations, the aqueous [Im₂₁][OAc] solution is found to promote the highest globular isoform population in AuIB.

Replica Exchange Molecular Dynamics: A Practical Application Protocol with Solutions to Common Problems and a Peptide Aggregation and Self-Assembly Example

Protein aggregation is associated with many human diseases such as Alzheimer's disease (AD), Parkinson's disease (PD), and type II diabetes (T2D). Understanding the molecular mechanism of protein aggregation is essential for therapy development. Molecular dynamics (MD) simulations have been shown as powerful tools to study protein aggregation. However, conventional MD simulations can hardly sample the whole conformational space of complex protein systems within acceptable simulation time as it can be easily trapped in local minimum-energy states. Many enhanced sampling methods have been developed. Among these, the replica exchange molecular dynamics (REMD) method has gained great popularity. By combining MD simulation with the Monte Carlo algorithm, the REMD method is capable of overcoming high energy-barriers easily and of sampling sufficiently the conformational space of proteins. In this chapter, we present a brief introduction to REMD method and a practical application protocol with a case study of the dimerization of the 11-25 fragment of human islet amyloid polypeptide (hIAPP(11-25)), using the GROMACS software. We also provide solutions to problems that are often encountered in practical use, and provide some useful scripts/commands from our research that can be easily adapted to other systems.

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.

Multiscale implementation of infinite-swap replica exchange molecular dynamics

Replica exchange molecular dynamics (REMD) is a popular method to accelerate conformational sampling of complex molecular systems. The idea is to run several replicas of the system in parallel at different temperatures that are swapped periodically. These swaps are typically attempted every few MD steps and accepted or rejected according to a Metropolis-Hastings criterion. This guarantees that the joint distribution of the composite system of replicas is the normalized sum of the symmetrized product of the canonical distributions of these replicas at the different temperatures. Here we propose a different implementation of REMD in which (i) the swaps obey a continuous-time Markov jump process implemented via Gillespie's stochastic simulation algorithm (SSA), which also samples exactly the aforementioned joint distribution and has the advantage of being rejection free, and (ii) this REMD-SSA is combined with the heterogeneous multiscale method to accelerate the rate of the swaps and reach the so-called infinite-swap limit that is known to optimize sampling efficiency. The method is easy to implement and can be trivially parallelized. Here we illustrate its accuracy and efficiency on the examples of alanine dipeptide in vacuum and C-terminal β-hairpin of protein G in explicit solvent. In this latter example, our results indicate that the landscape of the protein is a triple funnel with two folded structures and one misfolded structure that are stabilized by H-bonds.

Claws, Disorder, and Conformational Dynamics of the C-Terminal Region of Human Desmoplakin

Multicellular organisms consist of cells that interact via elaborate adhesion complexes. Desmosomes are membrane-associated adhesion complexes that mechanically tether the cytoskeletal intermediate filaments (IFs) between two adjacent cells, creating a network of tough connections in tissues such as skin and heart. Desmoplakin (DP) is the key desmosomal protein that binds IFs, and the DP·IF association poses a quandary: desmoplakin must stably and tightly bind IFs to maintain the structural integrity of the desmosome. Yet, newly synthesized DP must traffic along the cytoskeleton to the site of nascent desmosome assembly without "sticking" to the IF network, implying weak or transient DP···IF contacts. Recent work reveals that these contacts are modulated by post-translational modifications (PTMs) in DP's C-terminal tail (DPCTT). Using molecular dynamics simulations, we have elucidated the structural basis of these PTM-induced effects. Our simulations, nearing 2 μs in aggregate, indicate that phosphorylation of S2849 induces an "arginine claw" in desmoplakin's C-terminal tail. If a key arginine, R2834, is methylated, the DPCTT preferentially samples conformations that are geometrically well-suited as substrates for processive phosphorylation by the cognate kinase GSK3. We suggest that DPCTT is a molecular switch that modulates, via its conformational dynamics, DP's overall efficacy as a substrate for GSK3. Finally, we show that the fluctuating DPCTT can contact other parts of DP, suggesting a competitive binding mechanism for the modulation of DP···IF interactions.

Simulating Replica Exchange: Markov State Models, Proposal Schemes, and the Infinite Swapping Limit

Replica exchange molecular dynamics is a multicanonical simulation technique commonly used to enhance the sampling of solvated biomolecules on rugged free energy landscapes. While replica exchange is relatively easy to implement, there are many unanswered questions about how to use this technique most efficiently, especially because it is frequently the case in practice that replica exchange simulations are not fully converged. A replica exchange cycle consists of a series of molecular dynamics steps of a set of replicas moving under different Hamiltonians or at different thermodynamic states followed by one or more replica exchange attempts to swap replicas among the different states. How the replica exchange cycle is constructed affects how rapidly the system equilibrates. We have constructed a Markov state model of replica exchange (MSMRE) using long molecular dynamics simulations of a host-guest binding system as an example, in order to study how different implementations of the replica exchange cycle can affect the sampling efficiency. We analyze how the number of replica exchange attempts per cycle, the number of MD steps per cycle, and the interaction between the two parameters affects the largest implied time scale of the MSMRE simulation. The infinite swapping limit is an important concept in replica exchange. We show how to estimate the infinite swapping limit from the diagonal elements of the exchange transition matrix constructed from MSMRE "simulations of simulations" as well as from relatively short runs of the actual replica exchange simulations.

Intermediate Thermodynamic States Contribute Equally to Free Energy Convergence: A Demonstration with Replica Exchange

We investigate the relationship between the number of intermediate thermodynamic states along a pathway and the precision of free energy estimates. With a sufficient number of states, the asymptotic variance collapses as a function of the total sample size. Our analytical result is corroborated by replica exchange molecular dynamics simulations of model systems in which the neighbor exchange rate exceeds 35%. Precision collapse is also observed in heat capacity estimates based on the multistate Bennett acceptance ratio. In contrast to the relaxation and mean first-passage times, the autocorrelation time of state indices is found to be relevant to free energy convergence.

Peptide Bond Isomerization in High-Temperature Simulations

Force fields for molecular simulation are generally optimized to model macromolecules such as proteins at ambient temperature and pressure. Nevertheless, elevated temperatures are frequently used to enhance conformational sampling, either during system setup or as a component of an advanced sampling technique such as temperature replica exchange. Because macromolecular force fields are now put upon to simulate temperatures and time scales that greatly exceed their original design specifications, it is appropriate to re-evaluate whether these force fields are up to the task. Here, we quantify the rates of peptide bond isomerization in high-temperature simulations of three octameric peptides and a small fast-folding protein. We show that peptide octamers with and without proline residues undergo cis/trans isomerization every 1-5 ns at 800 K with three classical atomistic force fields (AMBER99SB-ILDN, CHARMM22/CMAP, and OPLS-AA/L). On the low microsecond time scale, these force fields permit isomerization of nonprolyl peptide bonds at temperatures ≥500 K, and the CHARMM22/CMAP force field permits isomerization of prolyl peptide bonds ≥400 K. Moreover, the OPLS-AA/L force field allows chiral inversion about the Cα atom at 800 K. Finally, we show that temperature replica exchange permits cis peptide bonds developed at 540 K to subsequently migrate back to the 300 K ensemble, where cis peptide bonds are present in 2 ± 1% of the population of Trp-cage TC5b, including up to 4% of its folded state. Further work is required to assess the accuracy of cis/trans isomerization in the current generation of protein force fields.

Replica exchange reactive molecular dynamics simulations of initial reactions in zeolite synthesis

Molecular simulation is a promising tool for the study of zeolite formation. However, sufficient sampling remains a grand challenge for the practical use of molecular simulation for this purpose. Here, we investigate the initial stage of zeolite synthesis under realistic conditions by using the replica-exchange method and the ReaxFF reactive force field. After a total simulation time of 480 ns, both energetic and structural properties approach convergence. Analyses of data collected at 600 K show that the inorganic structure directing agent NaOH promotes the aggregation of silicate, the formation of branched Si atoms and the formation of 5-membered rings. With the trajectories collected simultaneously at different temperatures, the effect of temperature is discussed.

Simulated Solute Tempering

For the enhanced conformational sampling in molecular dynamics (MD) simulations, we present "simulated solute tempering" (SST) which is an easy to implement variant of simulated tempering. SST extends conventional simulated tempering (CST) by key concepts of "replica exchange with solute tempering" (REST, Liu et al. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 13749). We have applied SST, CST, and REST to molecular dynamics (MD) simulations of an alanine octapeptide in explicit water. The weight parameters required for CST and SST are determined by two different formulas whose performance is compared. For SST only one of them yields a uniform sampling of the temperature space. Compared to CST and REST, SST provides the highest exchange probabilities between neighboring rungs in the temperature ladder. Concomitantly, SST leads to the fastest diffusion of the simulation system through the temperature space, in particular, if the "even-odd" exchange scheme is employed in SST. As a result, SST exhibits the highest sampling speed of the investigated tempering methods.

Simulations in generalized ensembles through noninstantaneous switches

Generalized-ensemble simulations, such as replica exchange and serial generalized-ensemble methods, are powerful simulation tools to enhance sampling of free energy landscapes in systems with high energy barriers. In these methods, sampling is enhanced through instantaneous transitions of replicas, i.e., copies of the system, between different ensembles characterized by some control parameter associated with thermodynamical variables (e.g., temperature or pressure) or collective mechanical variables (e.g., interatomic distances or torsional angles). An interesting evolution of these methodologies has been proposed by replacing the conventional instantaneous (trial) switches of replicas with noninstantaneous switches, realized by varying the control parameter in a finite time and accepting the final replica configuration with a Metropolis-like criterion based on the Crooks nonequilibrium work (CNW) theorem. Here we revise these techniques focusing on their correlation with the CNW theorem in the framework of Markovian processes. An outcome of this report is the derivation of the acceptance probability for noninstantaneous switches in serial generalized-ensemble simulations, where we show that explicit knowledge of the time dependence of the weight factors entering such simulations is not necessary. A generalized relationship of the CNW theorem is also provided in terms of the underlying equilibrium probability distribution at a fixed control parameter. Illustrative calculations on a toy model are performed with serial generalized-ensemble simulations, especially focusing on the different behavior of instantaneous and noninstantaneous replica transition schemes.

Large-scale asynchronous and distributed multidimensional replica exchange molecular simulations and efficiency analysis

We describe methods to perform replica exchange molecular dynamics (REMD) simulations asynchronously (ASyncRE). The methods are designed to facilitate large scale REMD simulations on grid computing networks consisting of heterogeneous and distributed computing environments as well as on homogeneous high-performance clusters. We have implemented these methods on NSF (National Science Foundation) XSEDE (Extreme Science and Engineering Discovery Environment) clusters and BOINC (Berkeley Open Infrastructure for Network Computing) distributed computing networks at Temple University and Brooklyn College at CUNY (the City University of New York). They are also being implemented on the IBM World Community Grid. To illustrate the methods, we have performed extensive (more than 60 ms in aggregate) simulations for the beta-cyclodextrin-heptanoate host-guest system in the context of one- and two-dimensional ASyncRE, and we used the results to estimate absolute binding free energies using the binding energy distribution analysis method. We propose ways to improve the efficiency of REMD simulations: these include increasing the number of exchanges attempted after a specified molecular dynamics (MD) period up to the fast exchange limit and/or adjusting the MD period to allow sufficient internal relaxation within each thermodynamic state. Although ASyncRE simulations generally require long MD periods (>picoseconds) per replica exchange cycle to minimize the overhead imposed by heterogeneous computing networks, we found that it is possible to reach an efficiency similar to conventional synchronous REMD, by optimizing the combination of the MD period and the number of exchanges attempted per cycle.

Exploring biomolecular dynamics and interactions using advanced sampling methods

Molecular dynamics (MD) and Monte Carlo (MC) simulations have emerged as a valuable tool to investigate statistical mechanics and kinetics of biomolecules and synthetic soft matter materials. However, major limitations for routine applications are due to the accuracy of the molecular mechanics force field and due to the maximum simulation time that can be achieved in current simulations studies. For improving the sampling a number of advanced sampling approaches have been designed in recent years. In particular, variants of the parallel tempering replica-exchange methodology are widely used in many simulation studies. Recent methodological advancements and a discussion of specific aims and advantages are given. This includes improved free energy simulation approaches and conformational search applications.

Computational Recipe for Efficient Description of Large-Scale Conformational Changes in Biomolecular Systems

Characterizing large-scale structural transitions in biomolecular systems poses major technical challenges to both experimental and computational approaches. On the computational side, efficient sampling of the configuration space along the transition pathway remains the most daunting challenge. Recognizing this issue, we introduce a knowledge-based computational approach toward describing large-scale conformational transitions using (i) nonequilibrium, driven simulations combined with work measurements and (ii) free energy calculations using empirically optimized biasing protocols. The first part is based on designing mechanistically relevant, system-specific reaction coordinates whose usefulness and applicability in inducing the transition of interest are examined using knowledge-based, qualitative assessments along with nonequilirbrium work measurements which provide an empirical framework for optimizing the biasing protocol. The second part employs the optimized biasing protocol resulting from the first part to initiate free energy calculations and characterize the transition quantitatively. Using a biasing protocol fine-tuned to a particular transition not only improves the accuracy of the resulting free energies but also speeds up the convergence. The efficiency of the sampling will be assessed by employing dimensionality reduction techniques to help detect possible flaws and provide potential improvements in the design of the biasing protocol. Structural transition of a membrane transporter will be used as an example to illustrate the workings of the proposed approach.

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.

Enhanced Monte Carlo Sampling through Replica Exchange with Solute Tempering

With a view to improving the consistency of free energy perturbation calculations in Monte Carlo simulations of protein–ligand complexes, we have implemented the replica exchange with solute tempering (REST) method in the MCPRO software. By augmenting the standard REST approach with regular attempted jumps in selected dihedral angles, our combined method facilitates sampling of ligand binding modes that are separated by high free energy barriers and ensures that computed free energy changes are considerably less dependent on the starting conditions and the chosen mutation pathway than those calculated with standard Monte Carlo sampling. We have applied the enhanced sampling method to the calculation of the activities of seven non-nucleoside inhibitors of HIV-1 reverse transcriptase, and its Tyr181Cys variant, and have shown that a range of binding orientations is possible depending on the nature of the ligand and the presence of mutations at the binding site.

Multidimensional Replica Exchange Molecular Dynamics Yields a Converged Ensemble of an RNA Tetranucleotide

A necessary step to properly assess and validate the performance of force fields for biomolecules is to exhaustively sample the accessible conformational space, which is challenging for large RNA structures. Given questions regarding the reliability of modeling RNA structure and dynamics with current methods, we have begun to use RNA tetranucleotides to evaluate force fields. These systems, though small, display considerable conformational variability and complete sampling with standard simulation methods remains challenging. Here we compare and discuss the performance of known variations of replica exchange molecular dynamics (REMD) methods, specifically temperature REMD (T-REMD), Hamiltonian REMD (H-REMD), and multidimensional REMD (M-REMD) methods, which have been implemented in Amber’s accelerated GPU code. Using two independent simulations, we show that M-REMD not only makes very efficient use of emerging large-scale GPU clusters, like Blue Waters at the University of Illinois, but also is critically important in generating the converged ensemble more efficiently than either T-REMD or H-REMD. With 57.6 μs aggregate sampling of a conformational ensemble with M-REMD methods, the populations can be compared to NMR data to evaluate force field reliability and further understand how putative changes to the force field may alter populations to be in more consistent agreement with experiment.

Infinite swapping replica exchange molecular dynamics leads to a simple simulation patch using mixture potentials

Replica exchange molecular dynamics (REMD) becomes more efficient as the frequency of swap between the temperatures is increased. Recently Plattner et al. [J. Chem. Phys. 135, 134111 (2011)] proposed a method to implement infinite swapping REMD in practice. Here we introduce a natural modification of this method that involves molecular dynamics simulations over a mixture potential. This modification is both simple to implement in practice and provides a better, energy based understanding of how to choose the temperatures in REMD to optimize efficiency. It also has implications for generalizations of REMD in which the swaps involve other parameters than the temperature.

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

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

Cellulase linkers are optimized based on domain type and function: insights from sequence analysis, biophysical measurements, and molecular simulation

Cellulase enzymes deconstruct cellulose to glucose, and are often comprised of glycosylated linkers connecting glycoside hydrolases (GHs) to carbohydrate-binding modules (CBMs). Although linker modifications can alter cellulase activity, the functional role of linkers beyond domain connectivity remains unknown. Here we investigate cellulase linkers connecting GH Family 6 or 7 catalytic domains to Family 1 or 2 CBMs, from both bacterial and eukaryotic cellulases to identify conserved characteristics potentially related to function. Sequence analysis suggests that the linker lengths between structured domains are optimized based on the GH domain and CBM type, such that linker length may be important for activity. Longer linkers are observed in eukaryotic GH Family 6 cellulases compared to GH Family 7 cellulases. Bacterial GH Family 6 cellulases are found with structured domains in either N to C terminal order, and similar linker lengths suggest there is no effect of domain order on length. O-glycosylation is uniformly distributed across linkers, suggesting that glycans are required along entire linker lengths for proteolysis protection and, as suggested by simulation, for extension. Sequence comparisons show that proline content for bacterial linkers is more than double that observed in eukaryotic linkers, but with fewer putative O-glycan sites, suggesting alternative methods for extension. Conversely, near linker termini where linkers connect to structured domains, O-glycosylation sites are observed less frequently, whereas glycines are more prevalent, suggesting the need for flexibility to achieve proper domain orientations. Putative N-glycosylation sites are quite rare in cellulase linkers, while an N-P motif, which strongly disfavors the attachment of N-glycans, is commonly observed. These results suggest that linkers exhibit features that are likely tailored for optimal function, despite possessing low sequence identity. This study suggests that cellulase linkers may exhibit function in enzyme action, and highlights the need for additional studies to elucidate cellulase linker functions.

Carbon nanotube inhibits the formation of β-sheet-rich oligomers of the Alzheimer's amyloid-β(16-22) peptide

Alzheimer's disease is associated with the abnormal self-assembly of the amyloid-β (Aβ) peptide into toxic β-rich aggregates. Experimental studies have shown that hydrophobic nanoparticles retard Aβ fibrillation by slowing down the nucleation process; however, the effects of nanoparticles on Aβ oligomeric structures remain elusive. In this study, we investigate the conformations of Aβ(16-22) octamers in the absence and presence of a single-walled carbon nanotube (SWCNT) by performing extensive all-atom replica exchange molecular-dynamics simulations in explicit solvent. Our simulations starting from eight random chains demonstrate that the addition of SWCNT into Aβ(16-22) solution prevents β-sheet formation. Simulation starting from a prefibrillar β-sheet octamer shows that SWCNT destabilizes the β-sheet structure. A detailed analysis of the Aβ(16-22)/SWCNT/water interactions reveals that both the inhibition of β-sheet formation and the destabilization of prefibrillar β-sheets by SWCNT result from the same physical forces: hydrophobic and π-stacking interactions (with the latter playing a more important role). By analyzing the stacking patterns between the Phe aromatic rings and the SWCNT carbon rings, we find that short ring-centroid distances mostly favor parallel orientation, whereas large distances allow all other orientations to be populated. Overall, our computational study provides evidence that SWCNT is likely to inhibit Aβ(16-22) and full-length Aβ fibrillation.

The O-glycosylated linker from the Trichoderma reesei Family 7 cellulase is a flexible, disordered protein

Fungi and bacteria secrete glycoprotein cocktails to deconstruct cellulose. Cellulose-degrading enzymes (cellulases) are often modular, with catalytic domains for cellulose hydrolysis and carbohydrate-binding modules connected by linkers rich in serine and threonine with O-glycosylation. Few studies have probed the role that the linker and O-glycans play in catalysis. Since different expression and growth conditions produce different glycosylation patterns that affect enzyme activity, the structure-function relationships that glycosylation imparts to linkers are relevant for understanding cellulase mechanisms. Here, the linker of the Trichoderma reesei Family 7 cellobiohydrolase (Cel7A) is examined by simulation. Our results suggest that the Cel7A linker is an intrinsically disordered protein with and without glycosylation. Contrary to the predominant view, the O-glycosylation does not change the stiffness of the linker, as measured by the relative fluctuations in the end-to-end distance; rather, it provides a 16 Å extension, thus expanding the operating range of Cel7A. We explain observations from previous biochemical experiments in the light of results obtained here, and compare the Cel7A linker with linkers from other cellulases with sequence-based tools to predict disorder. This preliminary screen indicates that linkers from Family 7 enzymes from other genera and other cellulases within T. reesei may not be as disordered, warranting further study.

Exchange Often and Properly in Replica Exchange Molecular Dynamics

Previous work by us showed that in replica exchange molecular dynamics, exchanges should be attempted extremely often, providing gains in efficiency and no undesired effects. Since that time some questions have been raised about the extendability of these claims to the general case. In this work, we answer this question in two ways. First, we perform a study measuring the effect of exchange attempt frequency in explicit solvent simulations including thousands of atoms. This shows, consistent with the previous assertion, that high exchange attempt frequency allows an optimal rate of exploration of configurational space. Second, we present an explanation of many theoretical and technical pitfalls when implementing replica exchange that cause "improper" exchanges resulting in erroneous data, exacerbated by high exchange attempt frequency.

Error and efficiency of simulated tempering simulations

We derive simple analytical expressions for the error and computational efficiency of simulated tempering (ST) simulations. The theory applies to the important case of systems whose dynamics at long times is dominated by the slow interconversion between two metastable states. An extension to the multistate case is described. We show that the relative gain in efficiency of ST simulations over regular molecular dynamics (MD) or Monte Carlo (MC) simulations is given by the ratio of their reactive fluxes, i.e., the number of transitions between the two states summed over all ST temperatures divided by the number of transitions at the single temperature of the MD or MC simulation. This relation for the efficiency is derived for the limit in which changes in the ST temperature are fast compared to the two-state transitions. In this limit, ST is most efficient. Our expression for the maximum efficiency gain of ST simulations is essentially identical to the corresponding expression derived by us for replica exchange MD and MC simulations [E. Rosta and G. Hummer, J. Chem. Phys. 131, 165102 (2009)] on a different route. We find quantitative agreement between predicted and observed efficiency gains in a test against ST and replica exchange MC simulations of a two-dimensional Ising model. Based on the efficiency formula, we provide recommendations for the optimal choice of ST simulation parameters, in particular, the range and number of temperatures, and the frequency of attempted temperature changes.