A simple method of estimating sampling consistency based on free energy map distance

Free energy surfaces, calculated during computer simulations, are known to be useful in characterizing the system of interest such as bio-molecules. However, it is usually very difficult to evaluate free energy from direct simulations, mainly because of high computational costs. Several simulation strategies, including replica exchange method (REM), have been developed to overcome this problem by providing efficient conformational sampling methods. Even with such efficient simulation schemes, fundamental questions concerning simulation convergence still remain to be resolved. In this paper, we propose to use a meta-distance between different free energy surfaces as one of the minimal measures for determining simulation consistency. This method is used for examining free energy surfaces obtained from folding simulations of a synthetic 11-residue protein (1AQG) using REM.