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.
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