Mathematical aspects of molecular replacement. III. Properties of space groups preferred by proteins in the Protein Data Bank.
The main goal of molecular replacement in macromolecular crystallography is to find the appropriate rigid-body transformations that situate identical copies of model proteins in the crystallographic unit cell. The search for such transformations can be thought of as taking place in the coset space Γ\G where Γ is the Sohncke group of the macromolecular crystal and G is the continuous group of rigid-body motions in Euclidean space. This paper, the third in a series, is concerned with viewing nonsymmorphic Γ in a new way. These space groups, rather than symmorphic ones, are the most common ones for protein crystals. Moreover, their properties impact the structure of the space Γ\G. In particular, nonsymmorphic space groups contain both Bieberbach subgroups and symmorphic subgroups. A number of new theorems focusing on these subgroups are proven, and it is shown that these concepts are related to the preferences that proteins have for crystallizing in different space groups, as observed in the Protein Data Bank.
Department of Mechanical Engineering, Whiting School of Engineering, Johns Hopkins University, Hackerman Hall 116, Baltimore, USA.
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Chirikjian
Department of Mechanical Engineering, Whiting School of Engineering, Johns Hopkins University, Hackerman Hall 116, Baltimore, USA.
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Sajjadi
Department of Biology, Krieger School of Arts and Sciences, Johns Hopkins University, 144 Mudd Hall, 3400 N. Charles St., Baltimore, MD 21218, USA.
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Toptygin
Department of Mechanical Engineering, Whiting School of Engineering, Johns Hopkins University, Hackerman Hall 116, Baltimore, USA.
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Yan
D018360:Crystallography, X-Ray; D030562:Databases, Protein; D008962:Models, Theoretical; D011487:Protein Conformation; D011506:Proteins / Q000737:chemistry*
D011506:Proteins
Bieberbach groups; Sohncke groups; normal subgroups; protein crystals