Free-energy calculations in protein folding by generalized-ensemble algorithms

We review uses of the generalized-ensemble algorithms for free-energy calculations in protein folding. Two of the well-known methods are multicanonical algorithm and replica-exchange method, the latter is also referred to as parallel tempering. We present a new generalized-ensemble algorithm that combines the merits of the two methods; it is referred to as the replica-exchange multicanonical algorithm. We also give a multidimensional extension of the replica-exchange method. Its realization as an umbrella sampling method, which we refer to as the replica-exchange umbrella sampling, is a powerful algorithm that can give free energy in wide reaction coordinate space.