J. Appl. Cryst. (2005). 38, 808-818 [ doi:10.1107/S002188980502474X ]
Abstract: Analytic expressions are presented for calculating translations of high-order three-dimensional expansions of orthonormal real spherical harmonic and Gaussian-type or exponential-type radial basis functions. When used with real spherical harmonic rotation matrices, the resulting translation matrices provide a fully analytic method of calculating six-dimensional real-space rotational-translational correlations. The correlation algorithm is demonstrated by using an exhaustive search to superpose the steric density functions of a pair of similar globular proteins in a matter of seconds on a contemporary personal computer. It is proposed that the techniques described could be used to accelerate the calculation of e.g. real-space electron density correlations in molecular replacement, docking proteins into electron microscopy density maps, and searching the Protein Data Bank for structural homologues.
Keywords: polar Fourier correlation; 6D correlation; fast Fourier transform; fast Hartley transform; spherical Bessel transform; Gaussian-type orbitals; Slater-type orbitals; exponential-type orbitals; Laguerre polynomials; protein shape; protein docking.
Copyright © International Union of Crystallography
IUCr Webmaster