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A Subgroup Algorithm To Identify Cross-Rotation Peaks Consistent With Non-Crystallographic Symmetry, Ryan H. Lilien, Chris Bailey-Kellogg, Amy C. Anderson, Bruce R. Donald

Dartmouth Scholarship

Molecular replacement (MR) often plays a prominent role in determining initial phase angles for structure determination by X-ray crystallography. In this paper, an efficient quaternion-based algorithm is presented for analyzing peaks from a cross-rotation function in order to identify model orientations consistent with proper non-crystallographic symmetry (NCS) and to generate proper NCS-consistent orientations missing from the list of cross-rotation peaks. The algorithm, CRANS, analyzes the rotation differences between each pair of cross-rotation peaks to identify finite subgroups. Sets of rotation differences satisfying the subgroup axioms correspond to orientations compatible with the correct proper NCS. The CRANS algorithm was first …