An Analysis on Protein Folding Problem by Replica-Exchange Method

Abstract

Because of the ruggedness of the energy landscape of protein systems, computer simulations of a protein folding process from the random-coil state to the native state is very difficult to achieve by the conventional molecular dynamics (MD) or Monte Carlo (MC) methods. 1) Recently, Replica-Exchange MC method 2) draws much attention as a promising algorithm that can overcome the multiple-minima problem. (This method is also referred to as replica Monte Carlo method, 3) multiple Markov chain method, 4) and parallel tempering. 5)) In this study, we have developed the MD version of Replica-Exchange method (Replica-Exchange MD method, REMD), 6) since in the system consisting of a protein and explicit water molecules, MD in the Cartesian coordinates is much easier to perform than MC. In REMD, we consider a generalized-ensemble with M non-interacting copies (or, replicas) of the original system in the canonical ensemble at M different inverse temperatures βm (m = 1, . . . ,M). The weight factor for the state X in this generalized ensemble, WREMD(X) is given by the product of Boltzmann factors for each replica, since the replicas are non-interacting. We now consider exchanging replicas i and j which are at βm and βn, respectively. In order for this exchange process to converge towards an equilibrium distribution, it is sufficient to impose the detailed balance condition on the transition probability w(X → X ′):