Fig. 1.

Schematic representation of FFT-based docking methods. In Cartesian FFT sampling (upper path), the ligand protein is translated along three Cartesian coordinates in Fourier space using the translational operator T. The translation must be repeated for each rotation of the ligand. In 5D FMFT docking (lower path), the direction of the vector from the center of the receptor to the center of the ligand is defined by two Euler angles, and the ligand is rotated around its center, resulting in the search space $\left(SO\left(3\right)\mathrm{\setminus }S\right)\times SO\left(3\right)$. All rotations are performed in generalized Fourier space, where D denotes the rotational operator. The only traditional search is the 1D translation along the vector between the centers of the two proteins.