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.
Original language | English |
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Pages (from-to) | 808-818 |
Number of pages | 10 |
Journal | Journal of Applied Crystallography |
Volume | 38 |
DOIs | |
Publication status | Published - 2005 |
Keywords
- SLATER-TYPE ORBITALS
- MOLECULAR-REPLACEMENT
- PROTEIN DOCKING
- CRYOELECTRON MICROSCOPY
- OVERLAP INTEGRALS
- SEARCH
- COMPUTATION
- ROTATION
- MACROMOLECULES
- IMPLEMENTATION