Superposition of molecules: Electron density fitting by application of Fourier transforms

In this article a new method is described to superimpose molecules using a crystallographic Fourier transform approach. Superimposed molecules, among other purposes, serve as a basis for three-dimensional (3D) QSAR analyses in drug design and therefore an objective and reproducible method of molecule alignment is of major importance. Fourier data are generated for hypothetical crystals of cubic symmetry for the compounds under consideration. A Patterson-density-based similarity index is used to optimize rotational alignment of the molecules. After optimization of rotational orientation, an electron density derived similarity index is used to further optimize overlap of electron density as a function of translation of the molecules. Both similarity indices are maximized by a simple optimization routine, thus enabling automated superposition. The use of Fourier space offers several advantages. First, rotational and translational parameters can be optimized separately, thus providing a small parameter space. Second, a limited number of data already provide an adequate, continuous description of the electron (or Patterson) density distribution. Third, crystallography provides simple methods to calculate the Fourier transforms that are needed. The resolution of the Patterson (electron) density representation used for superposition can be varied in a straightforward manner. Results are shown for the superposition of two antiviral agents, 2rs1 and 2r04; the dihydrofolate reductase ligands, methotrexate and dihydrofolate; and a set of three epsilon-thrombin inhibitors. (C) 1997 by John Wiley & Sons, Inc.