https://hal.inria.fr/inria-00434270Ritchie, DavidDavidRitchieDepartment of Computing Science - University of AberdeenHigh-order analytic translation matrix elements for real-space six-dimensional polar Fourier correlationsHAL CCSD2005[INFO.INFO-BI] Computer Science [cs]/Bioinformatics [q-bio.QM][SDV.BIBS] Life Sciences [q-bio]/Quantitative Methods [q-bio.QM][SDV.BBM.BC] Life Sciences [q-bio]/Biochemistry, Molecular Biology/Biochemistry [q-bio.BM]Ritchie, David2009-11-21 16:40:102017-11-28 15:18:032009-11-21 16:40:10enJournal articles10.1107/S002188980502474X1Analytic 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.