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 for
ces 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.
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 exchang
e 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 an improved prediction method of the tertiary structures of $alpha$-helical membrane proteins based on the replica-exchange method by taking into account helix deformations. Our method allows wide applications because transmembrane helices
of native membrane proteins are often distorted. In order to test the effectiveness of the present method, we applied it to the structure predictions of glycophorin A and phospholamban. The results were in accord with experiments.
