Multiple scaling replica exchange for the conformational sampling of biomolecules in explicit water

A multiple scaling replica exchange method for the efficient conformational sampling of biomolecular systems in explicit solvent is presented. The method is a combination of the replica exchange with solute tempering (REST) technique and a Tsallis biasing potential. The Tsallis biasing increases the sampling efficiency, while the REST minimizes the number of replicas needed. Unbiased statistics can be obtained by reweighting of the data using a weighted histogram analysis technique. The method is illustrated by its application to a ten residue peptide in explicit water.     

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.     

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.     

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.     

Asynchronous replica exchange for molecular simulations

An asynchronous implementation of the replica exchange method that addresses some of the limitations of conventional synchronous replica exchange implementations is presented. In asynchronous replica exchange pairs of processors initiate and perform temperature replica exchanges independently from the other processors, thereby removing the need for processor synchronization found in conventional synchronous implementations. Illustrative calculations on a molecular system are presented that show that asynchronous replica exchange, contrary to the synchronous implementation, is able to utilize at nearly top efficiency loosely coupled pools of processors with heterogeneous speeds, such as those found in computational grids and CPU scavenging environments. It is also shown that employing non-nearest-neighbor temperature exchanges, which are straightforward to implement within the asynchronous algorithm, can lead to faster temperature equilibration across processors.     

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.     

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.     

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.     

Effect of Cholesterol Molecules on Aβ1-42 Wild-Type and Mutants Trimers

Alzheimer’s disease displays aggregates of the amyloid-beta (Aβ) peptide in the brain, and there is increasing evidence that cholesterol may contribute to the pathogenesis of the disease. Though many experimental and theoretical studies have focused on the interactions of Aβ oligomers with membrane models containing cholesterol, an understanding of the effect of free cholesterol on small Aβ42 oligomers is not fully established. To address this question, we report on replica exchange with a solute tempering simulation of an Aβ42 trimer with cholesterol and compare it with a previous replica exchange molecular dynamics simulation. We show that the binding hot spots of cholesterol are rather complex, involving hydrophobic residues L17–F20 and L30–M35 with a non-negligible contribution of loop residues D22–K28 and N-terminus residues. We also examine the effects of cholesterol on the trimers of the disease-causing A21G and disease-protective A2T mutations by molecular dynamics simulations. We show that these two mutations moderately impact cholesterol-binding modes. In our REST2 simulations, we find that cholesterol is rarely inserted into aggregates but rather attached as dimers and trimers at the surface of Aβ42 oligomers. We propose that cholesterol acts as a glue to speed up the formation of larger aggregates; this provides a mechanistic link between cholesterol and Alzheimer’s disease.     

Velocity-scaling optimized replica exchange molecular dynamics of proteins in a hybrid explicit/implicit solvent

We propose a scheme for replica exchange molecular dynamics of proteins in explicit solvent that minimizes the number of required replicas using velocity rescaling. Our approach relies on a hybrid method where the protein evolves at each temperature in an explicit solvent, but replica exchange moves utilize an implicit solvent term. The two terms are coupled through the velocity rescaling. We test the efficiency of this approach for a common test case, the trp-cage protein.     

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.     

Lattice models of peptide aggregation: evaluation of conformational search algorithms

We present a series of conformational search calculations on the aggregation of short peptide fragments that form fibrils similar to those seen in many protein mis-folding diseases. The proteins were represented by a face-centered cubic lattice model with the conformational energies calculated using the Miyazawa-Jernigan potential. The searches were performed using algorithms based on the Metropolis Monte Carlo method, including simulated annealing and replica exchange. We also present the results of searches using the tabu search method, an algorithm that has been used for many optimization problems, but has rarely been used in protein conformational searches. The replica exchange algorithm consistently found more stable structures then the other algorithms, and was particularly effective for the octamers and larger systems.     

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.     

Hydrophobic aided replica exchange: an efficient algorithm for protein folding in explicit solvent

A hydrophobic aided replica exchange method (HAREM) is introduced to accelerate the simulation of all-atom protein folding in explicit solvent. This method is based on exaggerating the hydrophobic effect of various protein amino acids in water by attenuating the protein-water attractive interactions (mimicking the Chaperon effect) while leaving other interactions among protein atoms and water molecules unchanged. The method is applied to a small representative protein, the alpha-helix 3K(I), and it is found that the HAREM method successfully folds the protein within 4 ns, while the regular replica exchange method does not fold the same protein within 5 ns, even with many more replicas.     

Replica exchange with nonequilibrium switches: enhancing equilibrium sampling by increasing replica overlap

We describe a replica exchange strategy where trial swap configurations are generated by nonequilibrium switching simulations. By devoting simulation time to the switching simulations, one can systematically increase an effective overlap between replicas, which leads to an increased exchange acceptance rate and less correlated equilibrium samples. In this paper, we derive our method for a general class of stochastic dynamics, and discuss various strategies for enhancing replica overlap through novel dynamical schemes and prudent choices of switching protocols. We then demonstrate our method on a model system of alanine dipeptide in implicit solvent, characterizing decreases in data correlations and gains in sampling efficiency.     

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.     

Replica exchange with guided annealing for accelerated sampling of disordered protein conformations

We critically examine a recently proposed convective replica exchange (cRE) method for enhanced sampling of protein conformation based on theoretical and numerical analysis. The results demonstrate that cRE and related replica exchange with guided annealing (RE‐GA) schemes lead to unbalanced exchange attempt probabilities and break detailed balance whenever the system undergoes slow conformational transitions (relative to the temperature diffusion timescale). Nonetheless, numerical simulations suggest that approximate canonical ensembles can be generated for systems with small conformational transition barriers. This suggests that RE‐GA maybe suitable for simulating intrinsically disordered proteins, an important class of newly recognized functional proteins. The efficacy of RE‐GA is demonstrated by calculating the conformational ensembles of intrinsically disordered kinase inducible domain protein. The results show that RE‐GA helps the protein to escape nonspecific compact states more efficiently and provides several fold speedups in generating converged and largely correct ensembles compared to the standard temperature RE. © 2014 Wiley Periodicals, Inc.     

A divide-and-conquer strategy to improve diffusion sampling in generalized ensemble simulations

Generalized ensemble simulations generally suffer from the associated diffusion-sampling problem; the increased entropic barrier can greatly abolish sampling efficiency, in particular, with the increase of number of degrees of freedom in the target conformational space. Taking advantage of the recent simulated scaling method, we formulate a divide-and-conquer sampling strategy to solve this problem so as to robustly improve the sampling efficiency in generalized ensemble simulations. In the present method, the target conformational space sampling enhancement is decomposed to the sampling enhancements of several subconformational regions, and multiple independent SS simulations are performed to establish the individual sampling enhancement for each of the subconformational regions; in order to realize the global importance sampling, structure exchanges among these replicas are performed based on the Monte Carlo acceptance/rejection procedure. As demonstrated in our studies, the present divide-and-conquer sampling algorithm, named by us as "simulated scaling based variant Hamiltonian replica exchange method," has superior sampling capability so as to possibly play an essential role in dealing with the present bottleneck of generalized ensemble method developments: the system size limitations.     

Hamiltonian replica‐exchange simulations with adaptive biasing of peptide backbone and side chain dihedral angles

A Hamiltonian Replica‐Exchange Molecular Dynamics (REMD) simulation method has been developed that employs a two‐dimensional backbone and one‐dimensional side chain biasing potential specifically to promote conformational transitions in peptides. To exploit the replica framework optimally, the level of the biasing potential in each replica was appropriately adapted during the simulations. This resulted in both high exchange rates between neighboring replicas and improved occupancy/flow of all conformers in each replica. The performance of the approach was tested on several peptide and protein systems and compared with regular MD simulations and previous REMD studies. Improved sampling of relevant conformational states was observed for unrestrained protein and peptide folding simulations as well as for refinement of a loop structure with restricted mobility of loop flanking protein regions. © 2013 Wiley Periodicals, Inc.