Multidimensional generalized-ensemble algorithms for complex systems.
We give general formulations of the multidimensional multicanonical algorithm, simulated tempering, and replica-exchange method. We generalize the original potential energy function E(0) by adding any physical quantity V of interest as a new energy term. These multidimensional generalized-ensemble algorithms then perform a random walk not only in E(0) space but also in V space. Among the three algorithms, the replica-exchange method is the easiest to perform because the weight factor is just a product of regular Boltzmann-like factors, while the weight factors for the multicanonical algorithm and simulated tempering are not a priori known. We give a simple procedure for obtaining the weight factors for these two latter algorithms, which uses a short replica-exchange simulation and the multiple-histogram reweighting techniques. As an example of applications of these algorithms, we have performed a two-dimensional replica-exchange simulation and a two-dimensional simulated-tempering simulation using an alpha-helical peptide system. From these simulations, we study the helix-coil transitions of the peptide in gas phase and in aqueous solution.
Mitsutake
Ayori
A
Department of Physics, Keio University, Yokohama, Kanagawa 223-8522, Japan. ayori@mail.rk.phys.keio.ac.jp
Okamoto
Yuko
Y
D000465:Algorithms; D003198:Computer Simulation; D008958:Models, Molecular; D010455:Peptides / Q000737:chemistry; D017433:Protein Structure, Secondary; D012997:Solvents / Q000737:chemistry; D013696:Temperature; D013816:Thermodynamics; D013997:Time Factors
D010455:Peptides; D012997:Solvents