title: A subgroup algorithm to identify cross-rotation peaks consistent with non-crystallographic symmetry.
abstract: 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 tested using cross-rotation peaks computed from structure-factor data for three test systems and was 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 proper 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 proper NCS.
authors.affiliation: Dartmouth Computer Science Department, Hanover, NH 03755, USA.
authors.forename: Ryan H
authors.initials: RH
authors.lastname: Lilien
authors.forename: Chris
authors.initials: C
authors.lastname: Bailey-Kellogg
authors.forename: Amy C
authors.initials: AC
authors.lastname: Anderson
authors.forename: Bruce R
authors.initials: BR
authors.lastname: Donald
mesh_terms: D000465:Algorithms; D000818:Animals; D002772:Cholera Toxin / Q000737:chemistry; D003458:Cryptosporidium / Q000201:enzymology; D018360:Crystallography, X-Ray / Q000379:methods*; D019281:Dimerization; D008958:Models, Molecular; D009097:Multienzyme Complexes / Q000737:chemistry; D009154:Mutation; D011487:Protein Conformation; D013223:Statistics as Topic / Q000379:methods*; D013762:Tetrahydrofolate Dehydrogenase / Q000737:chemistry; D013940:Thymidylate Synthase / Q000737:chemistry; D014764:Viral Proteins / Q000737:chemistry
chemical_list: D009097:Multienzyme Complexes; D014764:Viral Proteins; C063473:gene 31 protein, Enterobacteria phage T4; C056930:thymidylate synthase-dihydrofolate reductase; D002772:Cholera Toxin; D013762:Tetrahydrofolate Dehydrogenase; D013940:Thymidylate Synthase