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Register a new userDesigned-walk replica-exchange method for simulations of complex systems
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We propose a new implementation of the replica-exchange method (REM) in which replicas follow a pre-planned route in temperature space instead of a random walk. Our method satisfies the detailed balance condition in the proposed route. The method forces tunneling events between the highest and lowest temperatures to happen with an almost constant period. The number of tunneling counts is proportional to that of the random-walk REM multiplied by the square root of moving distance in temperature space. We applied this new implementation to two kinds of REM and compared the results with those of the conventional random-walk REM. The test system was a two-dimensional Ising model, and our new method reproduced the results of the conventional random-walk REM and improved the tunneling counts by three times or more than that of the random-walk REM.
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We propose a replica-exchange method (REM) which does not use pseudo random numbers. For this purpose, we first give a conditional probability for Gibbs sampling replica-exchange method (GSREM) based on the heat bath method. In GSREM, replica exchange is performed by conditional probability based on the weight of states using pseudo random numbers. From the conditional probability, we propose a new method called deterministic replica-exchange method (DETREM) that produces thermal equilibrium distribution based on a differential equation instead of using pseudo random numbers. This method satisfies the detailed balance condition using a conditional probability of Gibbs heat bath method and thus results can reproduce the Boltzmann distribution within the condition of the probability. We confirmed that the equivalent results were obtained by REM and DETREM with two-dimensional Ising model. DETREM can avoid problems of choice of seeds in pseudo random numbers for REM using a differential equation.
We propose a new method for the determination of the weight factor for the simulated tempering method. In this method a short replica-exchange simulation is performed and the simulated tempering weight factor is obtained by the multiple-histogram reweighting techniques. The new algorithm is particularly useful for studying frustrated systems with rough energy landscape where the determination of the simulated tempering weight factor by the usual iterative process becomes very difficult. The effectiveness of the method is illustrated by taking an example for protein folding.
We propose two efficient algorithms for configurational sampling of systems with rough energy landscape. The first one is a new method for the determination of the multicanonical weight factor. In this method a short replica-exchange simulation is performed and the multicanonical weight factor is obtained by the multiple-histogram reweighting techniques. The second one is a further extension of the first in which a replica-exchange multicanonical simulation is performed with a small number of replicas. These new algorithms are particularly useful for studying the protein folding problem.
We propose a new method for molecular dynamics and Monte Carlo simulations, which is referred to as the replica-permutation method (RPM), to realize more efficient sampling than the replica-exchange method (REM).In RPM not only exchanges between two replicas but also permutations among more than two replicas are performed. Furthermore, instead of the Metropolis algorithm, the Suwa-Todo algorithm is employed for replica-permutation trials to minimize its rejection ratio. We applied RPM to particles in a double-well potential energy, Met-enkephalin in vacuum, and a C-peptide analog of ribonuclease A in explicit water. For a comparison purposes, replica-exchange molecular dynamics simulations were also performed. As a result, RPM sampled not only the temperature space but also the conformational space more efficiently than REM for all systems. From our simulations of C-peptide, we obtained the alpha-helix structure with salt-bridges between Gly2 and Arg10 which is known in experiments. Calculating its free-energy landscape, the folding pathway was revealed from an extended structure to the alpha-helix structure with the salt-bridges. We found that the folding pathway consists of the two steps: The first step is the salt-bridge formation step, and the second step is the alpha-helix formation step.
By combining two generalized-ensemble algorithms, Replica-Exchange Wang-Landau (REWL) method and 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 next. In order to verify the effectiveness of our protocol, we performed simulations of a square-lattice Ising model by the three methods, namely, REWL, MUCAREM, and REWL-MUCAREM. The results showed that the density of states obtained by the REWL-MUCAREM is more accurate than that is estimated by the two methods separately.
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