Efficient search for the possible mutual arrangements of two rigid bodies with the use of the generalized five-dimensional Fourier transform

A novel efficient algorithm for searching for the optimum arrangement of two rigid bodies is proposed. Such a problem often arises in the analysis of the matching of three-dimensional shapes (e.g., in protein-protein docking). The proposed method is based on exhaustive enumeration of the possible arrangements in the spherical polar Fourier space and uses the generalized five-dimensional Fourier transform to speed up the calculations. The main advantage of the described method consists in the efficiency of calculations performed with multicomponent evaluation functions. This high efficiency allows one to obtain highly accurate results with low computational costs.