In complex systems with many degrees of freedom such as peptides and proteins, there exists a huge number of local‐minimum‐energy states. Conventional simulations in the canonical ensemble are of little use, because they tend to get trapped in states of these energy local minima. A simulation in generalized ensemble performs a random walk in potential energy space and can overcome this difficulty. From only one simulation run, one can obtain canonical‐ensemble averages of physical quantities as functions of temperature by the single‐histogram and/or multiple‐histogram reweighting techniques. In this article we review uses of the generalized‐ensemble algorithms in biomolecular systems. Three well‐known methods, namely, multicanonical algorithm, simulated tempering, and replica‐exchange method, are described first. Both Monte Carlo and molecular dynamics versions of the algorithms are given. We then present three new generalized‐ensemble algorithms that combine the merits of the above methods. The effectiveness of the methods for molecular simulations in the protein folding problem is tested with short peptide systems. © 2001 John Wiley & Sons, Inc. Biopolymers (Pept Sci) 60: 96–123, 2001

The replica-exchange multicanonical algorithm and the multicanonical replica-exchange method for molecular dynamics simulations have recently been developed. In the former method the multicanonical weight factor is determined from a short replica-exchange simulation with the multiple-histogram reweighting techniques. A long multicanonical production run with high statistics is then performed with this weight factor. In this method, the process of determining the multicanonical weight factor is faster and simpler than that in the usual iterative determination. The multicanonical replica-exchange method is a further extension of the first in which a replica-exchange multicanonical simulation is performed with a small number of replicas. In this paper, we give the formulations of these two methods for Monte Carlo simulations and demonstrate the effectiveness of these algorithms for a penta peptide in the gas phase.

In Paper I of this series the formulations of the replica-exchange multicanonical algorithm and the multicanonical replica-exchange method for Monte Carlo versions have been presented. The effectiveness of these algorithms were then tested with the system of a penta peptide, Met-enkephalin, in the gas phase. In this article the detailed comparisons of performances of these algorithms together with the regular replica-exchange method are made, taking a more complex system of a 17-residue helical peptide. It is shown that these two new algorithms are more efficient than the regular replica-exchange method.

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