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 Carl o procedure, that predicts the topology of the energy hyper-surface using s tatistical and empirical data, as a method to improve the sampling efficien cy. It calculates the Valley Function which goes along the valley between l ocal minima in the energy surface and then reinforces the sampling of the r egion near the Valley Function in Monte Carlo Procedure. Valley Restrained Monte Carlo procedure samples the minima and the path along the lowest ener gy barrier between local minima more frequently, it reduces trapping in loc al minima and increases the convergence rate. This method is successfully a pplied to a model energy surface, the blocked alanine dipeptide (Ac-Ala-NHM e) and the pentapeptide Met-enkeplain (H-Tyr-Gly-Gly-Phe-Met-OK). The compa rison 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.