Valley Restrained Monte Carlo Procedure as a Method to Improve Sampling Efficiency

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, it reduces trapping in local minima and increases the convergence rate. This method is successfully applied to a model energy surface, the blocked alanine dipeptide (Ac-Ala-NHMe) and the pentapeptide Met-enkeplain (H-Tyr-Gly-Gly-Phe-Met-OH). The comparison between Valley Restrained Monte Carlo Procedure and the conventional Metropolis Monte Carlo Method shows that the sampling efficiency of our new method is greater than that of conventional Metropolis Monte Carlo. It is expected that this increase in the efficiency will be large when the system is larger.