Efficient sampling in the conformational space is necessary to predict the native structures of proteins. The replica-exchange method (REM) is one of the most well-known methods among the generalized-ensemble algorithms which realize efficient sampling in the conformational space for biomolecular systems. By exchanging the temperatures between the replicas, random walks of the replicas in the temperature space are realized. Accordingly, the simulation can escape from local-minimum states.
We have recently proposed a better alternative to the REM, which we refer to as the replica-permutation method (RPM) . 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.
For a large biomolecular system such as a protein in explicit water, REM requires a large number of replicas. To overcome this difficulty, the Hamiltonian REM (HREM) was often utilized. In HREM, parameters in the Hamiltonian are exchanged between replicas. By exchanging parameters that are related only to specific degrees of freedom, the number of replicas can be reduces in comparison with the conventional REM.
We proposed a new generalized -ensemble algorithm, which we refer to as the Hamiltonian RPM (HRPM), recently . This method has advantages of RPM and HREM. We will introduce this HRPM in our presentation. The results of HRPM simulations with Aβ fragments will also be shown.
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