Replica exchange method

The system for the replica-exchange method (REM) consists of M noninteracting copies (or, replicas) of the original system in the canonical ensemble at M different temperatures Tm (m = 1. M). We arrange the replicas so that there is always exactly one replica at each temperature. Then there exists a one-to-one correspondence between replicas and temperatures the label i 

Because the replicas are noninteracting, the weight factor for the state X in this generalized ensemble is given by the product of Boltzmann factors for each replica (or at each temperature)  

We now consider exchanging a pair of replicas in this ensemble. Suppose we exchange replicas i and j, which are at temperatures Tm and Tn, respectively, 

and n are related by the permutation functions in (4.40), and the exchange of replicas introduces a new permutation function /  

In the original implementation of the replica-exchange method (REM) [67-69], Monte Carlo algorithm was used, and only the coordinates q (and the potential energy function E(q)) had to be taken into account. In molecular dynamics algorithm, on the other hand, we also have to deal with the momenta p. We proposed the following momentum assignment in (4.45) (and in (4.46)) [77]  

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Fukunishi, O. Watanabe Takada, S., On the Hamiltonian replica exchange method for efficient sampling of biomolecular systems application to protein structure prediction, J. Chem. Phys. 2002,116, 9058-9067... 

Fenwick, M. K. Escobedo, F. A., Expanded ensemble and replica exchange methods for simulation of protein-like systems, J. Chem. Phys. 2003,119, 11998-12010... 

Jang, S.M. Shin, S. Pak, Y., Replica-exchange method using the generalized effective potential, Phys. Rev. Lett. 2003, 91... 

Sugita, Y. Kitao, A. Okamoto, Y., Multidimensional replica-exchange method for free-energy calculations, J. Chem. Phys. 2000,113, 6042-6051... 

Without loss of generality, we can assume Tj < T2 < < Tm- A simulation of the replica-exchange method (REM) is then realized by alternately... 

We now present our multidimensional extension of REM, which we refer to as multidimensional replica-exchange method (MREM) [80]. The crucial observation that led to the new algorithm is As long as we have M noninteracting... 

Detailed formulations of the two well-known generalized-ensemble algorithms, namely, multicanonical algorithm (MUCA) and replica-exchange method (REM), were given. We then introduced further extensions of the above two methods. We have shown the effectiveness of these algorithms by applying them to various biomolecular systems. 

Additionally, non-Hamiltonian d5mamics can be used in applications/ methodologies such as Path-integral MD, replica-exchange methods, variable transformation techniques, free energy dynamics methods, and other new applications. Generating these alternative statistical ensembles from simulation requires the use of extended systems or extended phase space [9]. In these systems, the simulations do not only include the N coordinate and momentum vectors that are needed to describe a classical Ai-particle system, but they also include a set of additional control or extended variables that are used to drive the fluctuations required by the ensemble of interest. 

Replica exchange methods are typically expensive as they require many (sometimes hundreds) simulations to be run synchronously, often on a large supercomputer facility. Their advantage is that they allow us to accelerate sampling using a minimal amount of a priori knowledge about the specific transition under study. This contrasts with metadynamics, which is very cheap from a computational standpoint but requires physical insight to select proper CVs. 

H. Fukunishi, O. Watanabe, and S. Takada,/. Chem. Phys., 116(20), 9058-9067 (2002). On the Hamiltonian Replica Exchange Method for Efficient Sampling of Biomolecular Systems Application to Protein Structure Prediction. 

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