title: Intensity statistics in the presence of translational noncrystallographic symmetry.
abstract: In the case of translational noncrystallographic symmetry (tNCS), two or more copies of a component in the asymmetric unit of the crystal are present in a similar orientation. This causes systematic modulations of the reflection intensities in the diffraction pattern, leading to problems with structure determination and refinement methods that assume, either implicitly or explicitly, that the distribution of intensities is a function only of resolution. To characterize the statistical effects of tNCS accurately, it is necessary to determine the translation relating the copies, any small rotational differences in their orientations, and the size of random coordinate differences caused by conformational differences. An algorithm to estimate these parameters and refine their values against a likelihood function is presented, and it is shown that by accounting for the statistical effects of tNCS it is possible to unmask the competing statistical effects of twinning and tNCS and to more robustly assess the crystal for the presence of twinning.
authors: Department of Haematology, Cambridge Institute for Medical Research, Wellcome Trust/MRC Building, Hills Road, Cambridge CB2 0XY, England. rjr27@cam.ac.uk
authors: Randy J
authors: RJ
authors: Read
authors: Paul D
authors: PD
authors: Adams
authors: Airlie J
authors: AJ
authors: McCoy
mesh_terms: D001483:Base Sequence; D003198:Computer Simulation / Q000706:statistics & numerical data; D018360:Crystallography, X-Ray; D030562:Databases, Protein / Q000706:statistics & numerical data; D005583:Fourier Analysis; D016013:Likelihood Functions; D008958:Models, Molecular; D014176:Protein Biosynthesis; D011897:Random Allocation; D014961:X-Ray Diffraction / Q000706:statistics & numerical data
keywords: intensity statistics; maximum likelihood; translational noncrystallographic symmetry; twinning
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