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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 to identify model orientations consistent with
non-crystallographic symmetry (NCS), and to generate NCS-consistent
orientations missing from the list of cross-rotation peaks. Our
algorithm, CRANS, analyzes the rotation differences between each pair
of cross-rotation peaks to identify finite subgroups of NCS. Sets of
rotation differences satisfying the subgroup axioms correspond to
orientations compatible with the correct NCS. The CRANS algorithm was
first tested using cross-rotation peaks computed from structure factor
data for three test systems, and then used to assist in the de novo
structure determination of dihydrofolate reductase-thymidylate
synthase (DHFR-TS) from Cryptosporidium hominis. In every case, the
CRANS algorithm runs in seconds to identify orientations consistent
with the observed NCS and to generate missing orientations not present
in the cross-rotation peak list. The CRANS algorithm has application
in every molecular replacement phasing effort with NCS.
A revised version of this paper has been accepted for publication
and will appear in the journal Acta Crystallographica D:
Biological Crystallography. In press (2004).
Bibliographic citation for this report: [plain text] [BIB] [BibTeX] [Refer]
Or copy and paste:
Ryan H. Lilien, Chris Bailey-Kellogg, Amy A. Anderson, and Bruce R. Donald, "A Subgroup Algorithm to Identify Cross-Rotation Peaks Consistent with Non-Crystallographic Symmetry." Dartmouth Computer Science Technical Report TR2003-481, December 2003.
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