%0 Journal Article
%T Accurate Calculation of the Density of States near the Ground-State Energy of the Peptides Met-Enkephalin and with the Wang-Landau Method: Lessons Learned
%A Priya Singh
%A Pradipta Bandyopadhyay
%J Journal of Atomic and Molecular Physics
%D 2012
%R 10.1155/2012/782806
%X The Wang-Landau method estimates the relative density of states (DOS) by performing random walk in energy space. However, estimation of the DOS near the ground state minimum is highly challenging because of the dearth of states in the low-energy region compared to that at the high-energy region. Ideally the derivative of the logarithm of the DOS with respect to energy, which is proportional to the inverse of temperature, should become steeper with decrease in energy. However, in actual estimation of the DOS for molecular systems, it is nontrivial to achieve this. In the current work, the accuracy of the Wang-Landau method in estimating the DOS near the ground state minimum is investigated for two peptides, Met-enkephalin and (Alanine)5. It has been found that the steepness of the DOS can be achieved if the correct ground state energy is found, the bin used to discretize the energy space is extremely small (0.1£¿kcal/mol was used in the current case) and the energy range used to estimate the DOS is small. The findings of this work can help in devising new protocols for calculating the DOS with high accuracy near the ground state minimum for molecular systems. 1. Introduction The density of states (DOS) is a fundamental quantity to understand the thermodynamic properties of a system. For any molecular system except for the smallest ones, calculation of the DOS is an extremely difficult problem because of the high dimensionality of the system. The Wang-Landau (WL) technique is one popular method to estimate the DOS [1]. This method performs a random walk in the energy space and estimates the DOS based on the flat histogram of energy obtained from the random walk. Initially the WL method was used for discrete systems such as Ising spin model and Potts model [1¨C3]. Later it has been extended to molecular systems. Till now several applications of the WL method for protein systems have been reported. For instance, the dimerization of glycophorin A, stability of proteins inside a cage, and thermodynamic properties of peptides have been investigated by the WL method [4¨C6]. Recently Singh et al. have done a systematic investigation on the performance of two flavours of the WL method for two small peptides [7]. However, one practical issue with the WL method is the poor quality of the DOS at the low-energy region of the system. As the DOS increases extremely rapidly with the increase of energy, low-energy estimation of the DOS is often done poorly by the WL method. Another way of saying that is that the number of states in the low-energy region is much less than
%U http://www.hindawi.com/journals/jamp/2012/782806/