Generalized-ensemble Algorithms Research Articles

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

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

Efficient simulation protocol for determining the density of states: Combination of replica-exchange Wang-Landau method and multicanonical replica-exchange method.

By combining two generalized-ensemble algorithms, the replica-exchange Wang-Landau (REWL) method and the multicanonical replica-exchange method (MUCAREM), we propose an effective simulation protocol to determine the density of states with high accuracy. The new protocol is referred to as REWL-MUCAREM, and REWL is first performed and then MUCAREM is performed. In order to verify the effectiveness of our protocol, we performed simulations of a square-lattice Ising model using the three methods, namely REWL, MUCAREM, and REWL-MUCAREM. The results showed that the density of states obtained by REWL-MUCAREM is more accurate than that is estimated by the two methods separately.

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

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

Protein structure predictions by enhanced conformational sampling methods.

In this Special Festschrift Issue for the celebration of Professor Nobuhiro Gō’s 80th birthday, we review enhanced conformational sampling methods for protein structure predictions. We present several generalized-ensemble algorithms such as multicanonical algorithm, replica-exchange method, etc. and parallel Monte Carlo or molecular dynamics method with genetic crossover. Examples of the results of these methods applied to the predictions of protein tertiary structures are also presented.

Multisequence algorithm for coarse-grained biomolecular simulations: Exploring the sequence-structure relationship of proteins.

We consider a generalized-ensemble algorithm for coarse-grained simulations of biomolecules which allows the thermodynamic behavior of two or more sequences to be determined in a single multisequence run. By carrying out a random walk in sequence space, the method also enhances conformational sampling. Escape from local energy minima is accelerated by visiting sequences for which the minima are more shallow or absent. We test the method on an intermediate-resolution coarse-grained model for protein folding with 3 amino acid types and explore the potential for a large-scale coverage of sequence space by applying the method to sets of more than 1000 sequences. The resulting thermodynamic data are used to analyze the structures and stability properties of sequences covering the space between folds with different secondary structures.

On the use of mass scaling for stable and efficient simulated tempering with molecular dynamics.

Simulated tempering (ST) is a generalized-ensemble algorithm that employs trajectories exploring a range of temperatures to effectively sample rugged energy landscapes. When implemented using the molecular dynamics method, ST can require the use of short time steps for ensuring the stability of trajectories at high temperatures. To address this shortcoming, a mass-scaling ST (MSST) method is presented in which the particle mass is scaled in proportion to the temperature. Mass scaling in the MSST method leads to velocity distributions that are independent of temperature and eliminates the need for velocity scaling after the accepted temperature updates that are required in conventional ST simulations. The homogeneity in time scales with changing temperature improves the stability of simulations and allows for the use of longer time steps at high temperatures. As a result, the MSST is found to be more efficient than the standard ST method, particularly for cases in which a large temperature range is employed. © 2016 Wiley Periodicals, Inc.

High Pressure Effect on a Helical Peptide Studied by Simulated Tempering Molecular Dynamics Simulations

High pressure effect on proteins and peptides has recently been studied theoretically and experimentally to understand structural properties of proteins such as protein folding and the function of proteins. While some proteins are denatured under high pressure conditions, some peptides are more stable at high pressure than at atmospheric pressure. It is important to understand the molecular mechanism of pressure-induced structural changes of proteins and peptides.We studied pressure effect on the structure of a helical peptide by using molecular dynamics simulations. We used an AK16 peptide as a helical peptide. AK16 is more helical under high pressure conditions than at atmospheric pressure. Molecular simulations often get trapped in the local minimum states of the free energy. In order to overcome such difficulty, we used a generalized-ensemble algorithm, which gives more efficient sampling in a molecular simulation. The simulated tempering method for the isobaric-isothermal ensemble (Y. Mori and Y. Okamoto, JPSJ 79, 074003, 2010) was used for efficient sampling in pressure space.We performed molecular dynamics simulations with the simulated tempering method for the system of AK16 in explicit water molecules. We found that the population of the helical structure of the peptide increases as pressure increases. We also calculated the free energy difference and the partial molar volume change as a function of pressure. The partial molar volume change from the helical state to the coil state increased monotonically from a negative value to a positive value with pressure. The positive value of the partial molar volume change is consistent with experimental results. We revealed the molecular details of AK16 under high pressure conditions (Y. Mori and H. Okumura, JPCL 4, 2079, 2013).

Surface-Tension Replica-Exchange Molecular Dynamics Method for Efficient Conformational Sampling of Biological Membrane Systems

Conformational sampling is fundamentally important for simulating complex bio-molecular systems. Generalized-ensemble algorithm, especially the temperature replica-exchange molecular dynamics method (REMD), is one of the widely used methods to explore structures of bio-molecules. Most temperature REMD simulations have focused on soluble proteins rather than membrane proteins or lipid bilayers, because explicit membranes do not keep their structural integrity at high temperature. Here, we propose a new generalized-ensemble algorithm for membrane systems, which we call the surface-tension REMD method. Each replica is simulated in the NPγT ensemble, where surface tensions in a pair of replicas are exchanged at certain intervals to enhance conformational sampling of the target membrane system. We tested our method on a fully hydrated DPPC lipid bilayer. During the simulation, a random walk in surface tension space is realized. Large-scale lateral deformation of DPPC membranes takes place in all of the replicas without collapse of the lipid bilayer structure. Our method could be applicable to a wide variety of biological membrane systems including mixed lipid bilayers and membrane-protein systems.

Surface-Tension Replica-Exchange Molecular Dynamics Method for Enhanced Sampling of Biological Membrane Systems.

Conformational sampling is fundamentally important for simulating complex biomolecular systems. The generalized-ensemble algorithm, especially the temperature replica-exchange molecular dynamics method (T-REMD), is one of the most powerful methods to explore structures of biomolecules such as proteins, nucleic acids, carbohydrates, and also of lipid membranes. T-REMD simulations have focused on soluble proteins rather than membrane proteins or lipid bilayers, because explicit membranes do not keep their structural integrity at high temperature. Here, we propose a new generalized-ensemble algorithm for membrane systems, which we call the surface-tension REMD method. Each replica is simulated in the NPγT ensemble, and surface tensions in a pair of replicas are exchanged at certain intervals to enhance conformational sampling of the target membrane system. We test the method on two biological membrane systems: a fully hydrated DPPC (1,2-dipalmitoyl-sn-glycero-3-phosphatidylcholine) lipid bilayer and a WALP23-POPC (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine) membrane system. During these simulations, a random walk in surface tension space is realized. Large-scale lateral deformation (shrinking and stretching) of the membranes takes place in all of the replicas without collapse of the lipid bilayer structure. There is accelerated lateral diffusion of DPPC lipid molecules compared with conventional MD simulation, and a much wider range of tilt angle of the WALP23 peptide is sampled due to large deformation of the POPC lipid bilayer and through peptide-lipid interactions. Our method could be applicable to a wide variety of biological membrane systems.

Pressure Effect on the Secondary Structure of Peptides Studied by Generalized-Ensemble Molecular Dynamics Simulations

Pressure effect on the structure of proteins and peptides has recently been studied theoretically and experimentally. Some proteins are denatured under high pressure conditions while some peptides are more stable in the folded state than in the random coil state at high pressure. It is important to understand the molecular mechanism of pressure-induced structural changes of proteins and peptides.We studied pressure effect on the structure of peptides by using molecular dynamics simulations. Molecular simulations often get trapped in the local minimum states of the free energy. In order to overcome such difficulty, we used a generalized-ensemble algorithm, which gives more efficient sampling in a molecular simulation.We performed molecular dynamics simulations with a generalized-ensemble algorithm for helical peptides in explicit water molecules. We found that the population of the secondary structure of the peptides changes as pressure increases. We also calculated the free energy as a function of pressure. The detail molecular mechanism of the structural change induced by pressure will be shown in the meeting.

Insights into Structural Properties of Denatured Human Prion 121-230 at Melting Temperature Studied by Replica Exchange Molecular Dynamics

Misfolding and aggregation of the prion protein (PrP) is responsible for the development of fatal transmissible neurodegenerative diseases. PrP undergoes structural conversion from a natively folded state into a misfolded state, resulting in aggregated amyloid fibrils. Partial unfolding has been recognized as an essential step in fibrillation, especially at the middle point of unfolding. To study the possible aggregation-prone states, we characterized the structure of the C-terminal globular domain of human prion (huPrP) 121-230 near extended conformation at melting temperature by replica exchange molecular dynamics (REMD) simulation, as the REMD method is the most suited generalized-ensemble algorithm that performs random walk in energy space and promotes a system to escape from local energy traps. Our results revealed that denatured huPrP is partially folded with α-helical structure at melting temperature. The simulation results provide further insight into the unfolding of prion, which is essential in pathogenesis of prion diseases.

Generalized-Ensemble Algorithms for Protein Folding and Unfolding

When one studies protein folding and unfolding by molecular simulations, one faces a great difficulty. Conventional simulations in the canonical ensemble are of little use, because they tend to get trapped in local-minimum-energy states, giving the results in error. A simulation in generalized ensemble performs a random walk in potential energy space and can overcome this difficulty. In this article we review some of powerful generalized-ensemble algorithms, namely, replica-exchange method, simulated tempering, and multicanonical algorithm, and their multidimensional/multivariable extensions. Keywords: Canonical ensemble, Generalized-ensemble algorithm, Isobaric-isothermal ensemble, Molecular dynamics (MD), Molecular simulation, Monte Carlo (MC), Multicanonical algorithm (MUCA), Multicanonical replica-exchange method (MUCAREM), Multidimensional generalized-ensemble algorithm, Pressure-induced denaturation, Protein folding, Protein unfolding, Replica-exchange method (REM), Replica-exchange molecular dynamics (REMD), Simulated tempering (ST)

Pressure-Induced Denaturation of Proteins Studied by Generalized-Ensemble Molecular Simulations

The pressure dependence of several proteins has recently been studied both experimentally and theoretically. Some of the experiments showed that proteins are denatured under high pressure conditions. We would like to understand the molecular mechanism of the pressure-induced denaturation of proteins by using molecular dynamics simulations.Molecular dynamics simulations have been widely used for studying biomolecular systems. However, the molecular simulations of biomolecular systems often get trapped in local minimum energy states. One way to overcome such a difficulty is to use generalized-ensemble algorithms. Using generalized-ensemble algorithms in molecular simulations, we can sample protein conformations efficiently and calculate physical quantities accurately. We have recently developed a generalized-ensemble algorithm for the isobaric-isothermal ensemble. This method can be used to calculate accurate temperature and pressure dependence of biomolecular systems.In this study we performed molecular simulations of ubiquitin, which is denatured under high pressure conditions. We performed generalized-ensemble molecular dynamics simulations by the NAMD program package. In these simulations, we used one temperature value, 300 K, and one hundred pressure values in range from 1 bar to 10,000 bar.We calculated the fluctuations of the distance between all pairs of amino acid residues. A large distance fluctuation of an amino acid pair means that increasing and decreasing pressure makes the amino acid residues move largely and therefore it is possible that local protein structure changes are induced with increasing and decreasing pressure. The amino acid residues which were largely displaced under high pressure conditions in the experiments correspond to the largely fluctuated amino acid residues in the molecular simulations.

Generalized-Ensemble Algorithms for Protein Folding and Unfolding

When one studies protein folding and unfolding by molecular simulations, one faces a great difficulty. Conventional simulations in the canonical ensemble are of little use, because they tend to get trapped in local-minimum-energy states, giving the results in error. A simulation in generalized ensemble performs a random walk in potential energy space and can overcome this difficulty. In this article we review some of powerful generalized-ensemble algorithms, namely, replica-exchange method, simulated tempering, and multicanonical algorithm, and their multidimensional/multivariable extensions.

3PT224 First principles molecular simulation with a generalized-ensemble algorithm for studying chemical reactions of biomolecular systems(The 50th Annual Meeting of the Biophysical Society of Japan)

3PT224 First principles molecular simulation with a generalized-ensemble algorithm for studying chemical reactions of biomolecular systems(The 50th Annual Meeting of the Biophysical Society of Japan)

Comparison of molecular dynamics simulation methods for amyloid β 1–42 monomers containing d-aspartic acid residues for predicting retention times in chromatography

Molecular dynamics simulations of amyloid β 1–42 containing d-aspartic acid residues were performed using several continuous solvent models to investigate the usefulness of simulation methods for d-amino acid-containing proteins and peptides. Normal molecular dynamics simulations and replica exchange molecular dynamics simulations, which are one of the generalized-ensemble algorithms, were performed. Because the β-structure contents of amyloid β 1–42 peptides obtained by replica exchange molecular dynamics simulations with Onufriev–Bashford–Case generalized Born implicit solvent were qualitatively consistent with experimental data, replica exchange molecular dynamics rather than other methods appeared to be more reasonable for calculations of amyloid β 1–42 containing d-aspartic acid residues. Computational results revealed that peptides with stereoinversion of Asp23 tend to form β-sheet structures by themselves, in contrast to the wild-type peptides that form β-sheet structures only after aggregation. These results are expected to be useful for computational investigations of proteins and peptides such as prediction of retention time of peptides and proteins containing d-aspartic acid residues.

Drug Design by Generalized-Ensemble Simulations

In pharmaceutical design based on molecular simulations, one faces a great difficulty. Conventional simulations in the canonical ensemble are of little use, because they tend to get trapped in some of the local-minimum-energy states that exist in a huge number. A simulation in generalized ensemble performs a random walk in potential energy space and can overcome this difficulty. In this article we review a few of powerful generalized-ensemble algorithms, namely, replica-exchange method, multidimensional replica-exchange method, and replica-exchange umbrella sampling. The effectiveness of the methods is tested with ligand and short peptide systems.

Multicanonical simulation and trapping due to high free-energy barriers in an Ising model for ultrathin magnetic films

Several studies to determine the nature of the thermodynamic phase transitions for an Ising model for ultrathin magnetic films have been reported in recent years. No conclusive results have been obtained yet, because the simulation with conventional Monte Carlo methods is slowed down by long relaxation times due to the suppression of tunneling events through free-energy barriers. In this paper we study the Ising model with dipolar interactions in two dimensions with an generalized-ensemble algorithm to address this problem. Herein, the multicanonical algorithm has been implemented in this study because it systematically explores energy configurations and enhances the rate of tunneling events. The success of a simulation depends on how often the algorithm explores the energy range between two extremal values. Our results indicate a limitation of the multicanonical algorithm in estimating the density of states for this model because the algorithm does not satisfactorily circumvent the problem of high free-energy barriers in the energy region where the nematic phase takes place.

Generalized-Ensemble Algorithms for the Isobaric–Isothermal Ensemble

We present generalized-ensemble algorithms for isobaric-isothermal molecular simulations. In addition to the multibaric-multithermal algorithm and replica-exchange method for the isobaric-isothermal ensemble, which have already been proposed, we propose a simulated tempering method for this ensemble. We performed molecular dynamics simulations with these algorithms for an alanine dipeptide system in explicit water molecules to test the effectiveness of the algorithms. We found that these generalized-ensemble algorithms are all useful for conformational sampling of biomolecular systems in the isobaric-isothermal ensemble.

Simulated Tempering Distributed Replica Sampling, Virtual Replica Exchange, and Other Generalized-Ensemble Methods for Conformational Sampling.

Generalized-ensemble algorithms in temperature space have become popular tools to enhance conformational sampling in biomolecular simulations. A random walk in temperature leads to a corresponding random walk in potential energy, which can be used to cross over energetic barriers and overcome the problem of quasi-nonergodicity. In this paper, we introduce two novel methods: simulated tempering distributed replica sampling (STDR) and virtual replica exchange (VREX). These methods are designed to address the practical issues inherent in the replica exchange (RE), simulated tempering (ST), and serial replica exchange (SREM) algorithms. RE requires a large, dedicated, and homogeneous cluster of CPUs to function efficiently when applied to complex systems. ST and SREM both have the drawback of requiring extensive initial simulations, possibly adaptive, for the calculation of weight factors or potential energy distribution functions. STDR and VREX alleviate the need for lengthy initial simulations, and for synchronization and extensive communication between replicas. Both methods are therefore suitable for distributed or heterogeneous computing platforms. We perform an objective comparison of all five algorithms in terms of both implementation issues and sampling efficiency. We use disordered peptides in explicit water as test systems, for a total simulation time of over 42 μs. Efficiency is defined in terms of both structural convergence and temperature diffusion, and we show that these definitions of efficiency are in fact correlated. Importantly, we find that ST-based methods exhibit faster temperature diffusion and correspondingly faster convergence of structural properties compared to RE-based methods. Within the RE-based methods, VREX is superior to both SREM and RE. On the basis of our observations, we conclude that ST is ideal for simple systems, while STDR is well-suited for complex systems.