Supercell refinement: a cautionary tale

Theoretically, crystals with supercells exist at a unique crossroads where they can be considered as either a large unit cell with closely spaced reflections in reciprocal space or a higher dimensional superspace with a modulation that is commensurate with the supercell. In the latter case, the structure would be defined as an average structure with functions representing a modulation to determine the atomic location in 3D space. Here, a model protein structure and simulated diffraction data were used to investigate the possibility of solving a real incommensurately modulated protein crystal using a supercell approximation. In this way, the answer was known and the refinement method could be tested. Firstly, an average structure was solved by using the `main' reflections, which represent the subset of the reflections that belong to the subcell and in general are more intense than the `satellite' reflections. The average structure was then expanded to create a supercell and refined using all of the reflections. Surprisingly, the refined solution did not match the expected solution, even though the statistics were excellent. Interestingly, the corresponding superspace group had multiple 3D daughter supercell space groups as possibilities, and it was one of the alternate daughter space groups that the refinement locked in on. The lessons learned here will be applied to a real incommensurately modulated profilin-actin crystal that has the same superspace group.