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 ofe.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.
Publisher
International Union of Crystallography (IUCr)
Subject
General Biochemistry, Genetics and Molecular Biology
Cited by
40 articles.
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