A straightforward application of Metropolis Monte Carlo method to a protein system has proven to be inefficient owing to the serious anisotropy of the conformational energy surface. We propose the Valley Restrained Monte Carlo procedure, that predicts the topology of the energy hyper-surface using statistical and empirical data, as a method to improve the sampling efficiency. It calculates the Valley Function which goes along the valley between local minima in the energy surface and then reinforces the sampling of the region near the Valley Function in Monte Carlo Procedure. Valley Restrained Monte Carlo procedure samples the minima and the path along the lowest energy barrier between local minima more frequently, thus it induces to get over the trapping in local minima and increase the convergence rate. This method is successfully applied to a model energy surface, the blocked alanine dipeptide(Ac-Ala-NHMe) and the pentapeptide Met-enkephalin(H-Tyr-Gly-Gly-Phe-Met-OH) systems. The comparison between Valley Restrained Monte Carlo Procedure and conventional Metropolis Monte Carlo Method shows that the sampling efficiency of our new method is found to be remarkably greater than that of the conventional Metropolis Monte Carlo Method. It is expected that this increase in the efficiency will be more prominent when the system is larger.
Taboo-based Monte Carlo procedure which restricts the sampling of the region near an old configuration, is developed. The feasibility of this method is tested on global optimization of a continuous model function and melting of the 256 Lennard-Jones particles at $T^*$=0.680 and $ρ^*$=0.850. From the comparison of results for the model function between our method and another method, we find the increase of convergence rate and the high possibility of escaping from the local energy minima. The results of the Lennard-Jones solids show that the convergence property to reach the equilibrium state is better than tha...