Replica exchange with dynamical scaling

A replica exchange method is presented which requires fewer replicas and is designed to be used for large systems. In this method, dynamically scaled replicas are placed between conventional replicas at broadly spaced temperatures. The potential of the scaled replicas is linearly scaled by a dynamical variable which varies between 0 and 1. When the variable is near either end point the replica can undergo exchanges with one of its neighboring replicas. Two different versions of the method are presented for a model system of a small peptide in water. The scaled replica can replace many replicas and the method can be up to ten times more efficient than conventional replica exchange.     

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. © 2015 Wiley Periodicals, Inc.     

Replica exchange with solute tempering: efficiency in large scale systems

We apply the recently developed replica exchange with solute tempering (REST) to three large solvated peptide systems: an alpha-helix, a beta-hairpin, and a TrpCage, with these peptides defined as the "central group". We find that our original implementation of REST is not always more efficient than the replica exchange method (REM). Specifically, we find that exchanges between folded (F) and unfolded (U) conformations with vastly different structural energies are greatly reduced by the nonappearance of the water self-interaction energy in the replica exchange acceptance probabilities. REST, however, is expected to remain useful for a large class of systems for which the energy gap between the two states is not large, such as weakly bound protein-ligand complexes. Alternatively, a shell of water molecules can be incorporated into the central group, as discussed in the original paper.     

Parallel replica dynamics with a heterogeneous distribution of barriers: application to n-hexadecane pyrolysis

Parallel replica dynamics simulation methods appropriate for the simulation of chemical reactions in molecular systems with many conformational degrees of freedom have been developed and applied to study the microsecond-scale pyrolysis of n-hexadecane in the temperature range of 2100-2500 K. The algorithm uses a transition detection scheme that is based on molecular topology, rather than energetic basins. This algorithm allows efficient parallelization of small systems even when using more processors than particles (in contrast to more traditional parallelization algorithms), and even when there are frequent conformational transitions (in contrast to previous implementations of the parallel replica algorithm). The parallel efficiency for pyrolysis initiation reactions was over 90% on 61 processors for this 50-atom system. The parallel replica dynamics technique results in reaction probabilities that are statistically indistinguishable from those obtained from direct molecular dynamics, under conditions where both are feasible, but allows simulations at temperatures as much as 1000 K lower than direct molecular dynamics simulations. The rate of initiation displayed Arrhenius behavior over the entire temperature range, with an activation energy and frequency factor of E(a) = 79.7 kcal/mol and log A/s(-1) = 14.8, respectively, in reasonable agreement with experiment and empirical kinetic models. Several interesting unimolecular reaction mechanisms were observed in simulations of the chain propagation reactions above 2000 K, which are not included in most coarse-grained kinetic models. More studies are needed in order to determine whether these mechanisms are experimentally relevant, or specific to the potential energy surface used.     

Convergence and sampling efficiency in replica exchange simulations of peptide folding in explicit solvent

Replica exchange methods (REMs) are increasingly used to improve sampling in molecular dynamics (MD) simulations of biomolecular systems. However, despite having been shown to be very effective on model systems, the application of REM in complex systems such as for the simulation of protein and peptide folding in explicit solvent has not been objectively tested in detail. Here we present a comparison of conventional MD and temperature replica exchange MD (T-REMD) simulations of a beta-heptapeptide in explicit solvent. This system has previously been shown to undergo reversible folding on the time scales accessible to MD simulation and thus allows a direct one-to-one comparison of efficiency. The primary properties compared are the free energy of folding and the relative populations of different conformers as a function of temperature. It is found that to achieve a similar degree of precision T-REMD simulations starting from a random set of initial configurations were approximately an order of magnitude more computationally efficient than a single 800 ns conventional MD simulation for this system at the lowest temperature investigated (275 K). However, whereas it was found that T-REMD simulations are more than four times more efficient than multiple independent MD simulations at one temperature (300 K) the actual increase in conformation sampling was only twofold. The overall gain in efficiency using REMD resulted primarily from the ordering of different conformational states over temperature, as opposed to a large increase of conformational sampling. It is also shown that in this system exchanges are accepted primarily based on (random) fluctuations within the solvent and are not strongly correlated with the instantaneous peptide conformation raising questions in regard to the efficiency of T-REMD in larger systems.     

How hot? Systematic convergence of the replica exchange method using multiple reservoirs

We have devised a systematic approach to converge a replica exchange molecular dynamics simulation by dividing the full temperature range into a series of higher temperature reservoirs and a finite number of lower temperature subreplicas. A defined highest temperature reservoir of equilibrium conformations is used to help converge a lower but still hot temperature subreplica, which in turn serves as the high‐temperature reservoir for the next set of lower temperature subreplicas. The process is continued until an optimal temperature reservoir is reached to converge the simulation at the target temperature. This gradual convergence of subreplicas allows for better and faster convergence at the temperature of interest and all intermediate temperatures for thermodynamic analysis, as well as optimizing the use of multiple processors. We illustrate the overall effectiveness of our multiple reservoir replica exchange strategy by comparing sampling and computational efficiency with respect to replica exchange, as well as comparing methods when converging the structural ensemble of the disordered Aβ_21‐30 peptide simulated with explicit water by comparing calculated Rotating Overhauser Effect Spectroscopy intensities to experimentally measured values. © 2009 Wiley Periodicals, Inc. J Comput Chem 31: 620–627, 2010     

Replica exchanging self-guided Langevin dynamics for efficient and accurate conformational sampling

This work presents a replica exchanging self-guided Langevin dynamics (RXSGLD) simulation method for efficient conformational searching and sampling. Unlike temperature-based replica exchanging simulations, which use high temperatures to accelerate conformational motion, this method uses self-guided Langevin dynamics (SGLD) to enhance conformational searching without the need to elevate temperatures. A RXSGLD simulation includes a series of SGLD simulations, with simulation conditions differing in the guiding effect and∕or temperature. These simulation conditions are called stages and the base stage is one with no guiding effect. Replicas of a simulation system are simulated at the stages and are exchanged according to the replica exchanging probability derived from the SGLD partition function. Because SGLD causes less perturbation on conformational distribution than high temperatures, exchanges between SGLD stages have much higher probabilities than those between different temperatures. Therefore, RXSGLD simulations have higher conformational searching ability than temperature based replica exchange simulations. Through three example systems, we demonstrate that RXSGLD can generate target canonical ensemble distribution at the base stage and achieve accelerated conformational searching. Especially for large systems, RXSGLD has remarkable advantages in terms of replica exchange efficiency, conformational searching ability, and system size extensiveness.     

Serial replica exchange

Parallel tempering (or the replica exchange method (REM)) is a powerful method for speeding up the sampling of conformational states of systems with rough energy landscapes, like proteins, where stable conformational states can be separated by large energy barriers. The usual implementation of the REM is performed on local computer clusters (or parallel processors) where the different replicas must be run synchronously. Here, we present serial replica exchange (SREM), a method that is equivalent to the standard REM in terms of efficiency yet runs asynchronously on a distributed network of computers. A second advantage is the method's greatly enhanced fault tolerance, which enables the study of biological systems on worldwide distributed computing environments, such as Folding@Home. For proof of concept, we apply the SREM to a single alanine dipeptide molecule in explicit water. We show that the SREM reproduces the thermodynamic and structural properties determined by the REM.     

The temperature intervals with global exchange of replicas empirical accelerated sampling method: parameter sensitivity and extension to a complex molecular system

The recently developed "temperature intervals with global exchange of replicas" (TIGER2) algorithm is an efficient replica-exchange sampling algorithm that provides the freedom to specify the number of replicas and temperature levels independently of the size of the system and temperature range to be spanned, thus making it particularly well suited for sampling molecular systems that are considered to be too large to be sampled using conventional replica exchange methods. Although the TIGER2 method is empirical in nature, when appropriately applied it is able to provide sampling that satisfies the balance condition and closely approximates a Boltzmann-weighted ensemble of states. In this work, we evaluated the influence of factors such as temperature range, temperature spacing, replica number, and sampling cycle design on the accuracy of a TIGER2 simulation based on molecular dynamics simulations of alanine dipeptide in implicit solvent. The influence of these factors is further examined by calculating the properties of a complex system composed of the B1 immunoglobulin-binding domain of streptococcal protein G (protein G) in aqueous solution. The accuracy of a TIGER2 simulation is particularly sensitive to the maximum temperature level selected for the simulation. A method to determine the appropriate maximum temperature level to be used in a TIGER2 simulation is presented.     

Finite reservoir replica exchange to enhance canonical sampling in rugged energy surfaces

A "finite reservoir" replica exchange method is presented to further enhance sampling upon the regular replica exchange method (REM) in a rugged energy surface. The present method can facilitate important sampling more efficiently by exchanging structures with configurations randomly selected from a finite-sized reservoir; this finite reservoir is pregenerated and updated by a mechanism of replica exchange with neighboring "temperature" simulations. In practice, this proposal revises exchange schedule in REM simulations in order to make productive exchange for conformational "tunneling" more frequent.     

Comparison of two adaptive temperature-based replica exchange methods applied to a sharp phase transition of protein unfolding-folding

Temperature-based replica exchange (T-ReX) enhances sampling of molecular dynamics simulations by autonomously heating and cooling simulation clients via a Metropolis exchange criterion. A pathological case for T-ReX can occur when a change in state (e.g., folding to unfolding of a protein) has a large energetic difference over a short temperature interval leading to insufficient exchanges amongst replica clients near the transition temperature. One solution is to allow the temperature set to dynamically adapt in the temperature space, thereby enriching the population of clients near the transition temperature. In this work, we evaluated two approaches for adapting the temperature set: a method that equalizes exchange rates over all neighbor temperature pairs and a method that attempts to induce clients to visit all temperatures (dubbed "current maximization") by positioning many clients at or near the transition temperature. As a test case, we simulated the 57-residue SH3 domain of alpha-spectrin. Exchange rate equalization yielded the same unfolding-folding transition temperature as fixed-temperature ReX with much smoother convergence of this value. Surprisingly, the current maximization method yielded a significantly lower transition temperature, in close agreement with experimental observation, likely due to more extensive sampling of the transition state.     

Replica state exchange metadynamics for improving the convergence of free energy estimates

Metadynamics (MTD) is a powerful enhanced sampling method for systems with rugged energy landscapes. It constructs a bias potential in a predefined collective variable (CV) space to overcome barriers between metastable states. In bias‐exchange MTD (BE‐MTD), multiple replicas approximate the CV space by exchanging bias potentials (replica conditions) with the Metropolis–Hastings (MH) algorithm. We demonstrate that the replica‐exchange rates and the convergence of free energy estimates of BE‐MTD are improved by introducing the infinite swapping (IS) or the Suwa‐Todo (ST) algorithms. Conceptually, IS and ST perform transitions in a replica state space rather than exchanges in a replica condition space. To emphasize this, the proposed scheme is called the replica state exchange MTD (RSE‐MTD). Benchmarks were performed with alanine polypeptides in vacuum and water. For the systems tested in this work, there is no significant performance difference between IS and ST. © 2015 Wiley Periodicals, Inc.     

Hybrid Hamiltonian replica exchange molecular dynamics simulation method employing the Poisson-Boltzmann model

A hybrid Hamiltonian replica exchange molecular dynamics simulation scheme based on explicit water model hybrided with Poisson-Boltzmann model is brought out. In this method the motions of atoms are governed by potential energy obtained from explicit water model. However, the exchanges between different replicas under different temperatures are controlled by the solvation energies of the solute calculated using the Poisson-Boltzmann model. In order to get the correct canonical ensembles, the van der Waals radii, which are used to define the dielectric boundary, have to be optimized. The conformational spaces of three distinct pentapeptides, Met-enkephalin, alanine 5, and glycine 5, are explored. We find that with the optimized radii the structural ensembles are nearly identical to those obtained by standard replica exchange simulations while the number of replica needed is reduced greatly.     

Sampling enhancement for the quantum mechanical potential based molecular dynamics simulations: a general algorithm and its extension for free energy calculation on rugged energy surface

An approach is developed in the replica exchange framework to enhance conformational sampling for the quantum mechanical (QM) potential based molecular dynamics simulations. Importantly, with our enhanced sampling treatment, a decent convergence for electronic structure self-consistent-field calculation is robustly guaranteed, which is made possible in our replica exchange design by avoiding direct structure exchanges between the QM-related replicas and the activated (scaled by low scaling parameters or treated with high "effective temperatures") molecular mechanical (MM) replicas. Although the present approach represents one of the early efforts in the enhanced sampling developments specifically for quantum mechanical potentials, the QM-based simulations treated with the present technique can possess the similar sampling efficiency to the MM based simulations treated with the Hamiltonian replica exchange method (HREM). In the present paper, by combining this sampling method with one of our recent developments (the dual-topology alchemical HREM approach), we also introduce a method for the sampling enhanced QM-based free energy calculations.     

On the efficiency of exchange in parallel tempering monte carlo simulations

We introduce the concept of effective fraction, defined as the expected probability that a configuration from the lowest index replica successfully reaches the highest index replica during a replica exchange Monte Carlo simulation. We then argue that the effective fraction represents an adequate measure of the quality of the sampling technique, as far as swapping is concerned. Under the hypothesis that the correlation between successive exchanges is negligible, we propose a technique for the computation of the effective fraction, a technique that relies solely on the values of the acceptance probabilities obtained at the end of the simulation. The effective fraction is then utilized for the study of the efficiency of a popular swapping scheme in the context of parallel tempering in the canonical ensemble. For large dimensional oscillators, we show that the swapping probability that minimizes the computational effort is 38.74%. By studying the parallel tempering swapping efficiency for a 13-atom Lennard-Jones cluster, we argue that the value of 38.74% remains roughly the optimal probability for most systems with continuous distributions that are likely to be encountered in practice.     

Temperature weighted histogram analysis method, replica exchange, and transition paths

We analyzed the data from a replica exchange molecular dynamics simulation using the weighted histogram analysis method to combine data from all of the temperature replicas (T-WHAM) to obtain the room-temperature potential of mean force of the G-peptide (the C-terminal beta-hairpin of the B1 domain of protein G) in regions of conformational space not sampled at room temperature. We were able to determine the potential of mean force in the transition region between a minor alpha-helical population and the major beta-hairpin population and identify a possible transition path between them along which the peptide retains a significant amount of secondary structure. This observation provides new insights into a possible mechanism of formation of beta-sheet secondary structures in proteins. We developed a novel Bayesian statistical uncertainty estimation method for any quantity derived from WHAM and used it to validate the calculated potential of mean force. The feasibility of estimating regions of the potential of mean force with unfavorable free energy at room temperature by T-WHAM analysis of replica exchange simulations was further tested on a system that can be solved analytically and presented some of the same challenges found in more complex chemical systems.     

On easy implementation of a variant of the replica exchange with solute tempering in GROMACS

To reduce the number of replicas required in the conventional replica exchange method for huge systems, recently the replica exchange with solute tempering (REST) method was proposed. Here we showed that a variant of REST realized by rescaling the force-field parameters can be performed with GROMACS 4 without changing the code. We tested the variant REST for alanine dipeptide and an N-terminal peptide from p53 confirming its performance nearly equal to the original REST.     

Modified replica exchange simulation methods for local structure refinement

Parallel tempering, also known as replica exchange molecular dynamics (REMD), has recently been successfully used to study the structure and thermodynamic properties of biomolecules such as peptides and small proteins. For large systems, however, applying REMD can be costly since the number of replicas needed increases as the square root of the number of degrees of freedom in the system. Often, enhanced sampling is only needed for a subset of atoms, such as a loop region of a large protein or a small ligand binding to a receptor. In such applications, it is often reasonable to assume a weak dependence of the structure of the larger region on the instantaneous conformation of the smaller region of interest. For these cases, we derived two variant replica exchange methods, partial replica exchange molecular dynamics (PREMD) and local replica exchange molecular dynamics (LREMD). The Hamiltonian for the system is separated, with replica exchange carried out only for terms involving the subsystem of interest while the remainder of the system is maintained at a single temperature. The number of replicas required for efficient exchange thus depends on the number of degrees of freedom in the fragment needing refinement rather than on the size of the full system. The method can be applied to much larger systems than was previously practical. This also provides a means to preserve the integrity of the structure outside the refinement region without introduction of restraints. LREMD takes this weak coupling approximation a step further, employing only a single representation of the large fragment that simultaneously interacts with all of the replicas of the subsystem of interest. This is obtained by combining replica exchange with the locally enhanced sampling approximation (LES), reducing the computational expense of replica exchange simulations to near that of a single standard molecular dynamics (MD) simulation. Use of LREMD also permits the use of LES without requiring the specification of a single temperature, a known difficulty for standard LES simulations. We tested these two methods on the loop region of an RNA hairpin model system and find significant advantages over standard MD and REMD simulations.     

A convective replica‐exchange method for sampling new energy basins

Replica‐exchange is a powerful simulation method for sampling the basins of a rugged energy landscape. The replica‐exchange method's sampling is efficient because it allows replicas to perform round trips in temperature space, thereby visiting both low and high temperatures in the same simulation. However, replicas have a diffusive walk in temperature space, and the round trip rate decreases significantly with the system size. These drawbacks make convergence of the simulation even more difficult than it already is when bigger systems are tackled. Here, we present a simple modification of the exchange method. In this method, one of the replicas steadily raises or lowers its temperature. We tested the convective replica‐exchange method on three systems of varying complexity: the alanine dipeptide in implicit solvent, the GB1 β‐hairpin in explicit solvent and the Aβ_25–35 homotrimer in a coarse grained representation. For the highly frustrated Aβ_25–35 homotrimer, the proposed “convective” replica‐exchange method is twice as fast as the standard method. It discovered 24 out of 27 free‐energy basins in less than 500 ns. It also prevented the formation of groups of replicas that usually form on either side of an exchange bottleneck, leading to a more efficient sampling of new energy basins than in the standard method. © 2012 Wiley Periodicals, Inc.