On some implications of non-crystallographic symmetry

The standard molecular replacement (MR) protocol involves one-by-one search for molecules composing the asymmetric unit, therefore the non-crystallographic symmetry (NCS) complicates the structure determination. However, the conservation of the oligomeric state in a series of homologues and the use of information about the NCS in the target crystal may help to solve difficult MR problems. A number of the NCS cases which have required tailor-made MR protocols for successful structure solution are presented in this thesis. The ultimate goal is to rationalise these approaches and implement them as supplementary pathways for MR pipelines. Intermolecular contacts in a macromolecular crystal can have substantially different strengths as, for example, in crystals composed of natural oligomers, or in order-disorder (OD) structures with stronger interactions within diperiodic OD-layers and weaker interactions between the layers. Symmetry of the tightly bound assemblies is often non-crystallographic, whereas weaker interactions are adjusted to enable three-dimensional translational symmetry in the crystal. Weaker interactions can vary between different crystal forms (polymorphs) or even within one crystal to give rise to NCS by translation, twinning or crystal disorder. Several twins, structures with translational NCS and OD-structures are presented in this thesis. In some cases, the relation between NCS and twinning gives an insight into the twin morphology. Two examples of macromolecular twins are discussed in which the NCS analysis explained the accidental lattice symmetry. In another case, the NCS defined the geometry of twinning by reticular merohedry, so an accurate detwinning was possible without precise measurements of relative orientation of the alternative lattices. The twin axis can be aligned with an NCS axis. High relative frequency of such twinning cases in the Protein Data Bank is demonstrated and the effect of such interference between twinning and NCS on the intensity statistics is analysed to provide guidelines for interpretation of the standard twinning tests. The alignment of NCS and twin axes is typical for OD-twins by metric merohedry and one of these twins is analysed in detail. Standard MR is easily adaptable to the case of the translational NCS without significant changes in the algorithm or protocol. However, translational NCS imposes a problem of falseorigin MR solution, as is demonstrated in this work. Three cases are described, in which such problem had occurred and was resolved, and which prompted to design the program Zanuda that automatically handles false-origin MR solutions and also enables validation and correction of the space group assignment in pseudosymmetric twins. Thus, the two distinct topics of this thesis are the NCS guided MR, and diagnostics of twinning and incorrect symmetry assignment. Both lines of research have a common goal, to extend the boundaries of existing methods of macromolecular structure solution.