Wang-Landau molecular dynamics technique to search for low-energy conformational space of proteins

Multicanonical molecular dynamics (MD) is a powerful technique for sampling conformations on rugged potential surfaces such as protein. However, it is notoriously difficult to estimate the multicanonical temperature effectively. Wang and Landau developed a convenient method for estimating the density of states based on a multicanonical Monte Carlo method. In their method, the density of states is calculated autonomously during a simulation. In this paper, we develop a set of techniques to effectively apply the Wang-Landau method to MD simulations. In the multicanonical MD, the estimation of the derivative of the density of states is critical. In order to estimate it accurately, we devise two original improvements. First, the correction for the density of states is made smooth by using the Gaussian distribution obtained by a short canonical simulation. Second, an approximation is applied to the derivative, which is based on the Gaussian distribution and the multiple weighted histogram technique. A test of this method was performed with small polypeptides, Met-enkephalin and Trp-cage, and it is demonstrated that Wang-Landau MD is consistent with replica exchange MD but can sample much larger conformational space.