  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".
