Accurate Estimation of the Entropy of Rotation-Translation Probability Distributions

The estimation of rotational and translational entropies in the context of ligand binding has been the subject of long-time investigations. The high dimensionality (six) of the problem and the limited amount of sampling often prevent the required resolution to provide accurate estimates by the histogram method. Recently, the nearest-neighbor distance method has been applied to the problem, but the solutions provided either address rotation and translation separately, therefore lacking correlations, or use a heuristic approach. Here we address rotational-translational entropy estimation in the context of nearest-neighbor-based entropy estimation, solve the problem numerically, and provide an exact and an approximate method to estimate the full rotational-translational entropy.