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High-order analytic translation matrix elements for real-space six-dimensional polar Fourier correlations

David Ritchie 1, *
* Corresponding author
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.
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https://hal.inria.fr/inria-00434270
Contributor : David Ritchie <>
Submitted on : Saturday, November 21, 2009 - 4:40:10 PM
Last modification on : Tuesday, November 28, 2017 - 3:18:03 PM

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David Ritchie. High-order analytic translation matrix elements for real-space six-dimensional polar Fourier correlations. Journal of Applied Crystallography, International Union of Crystallography, 2005, 38 (5), pp.808-818. ⟨10.1107/S002188980502474X⟩. ⟨inria-00434270⟩

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