Simulation of modulated reflections

In a modulated crystal, the repeating unit is not periodic but contains a disorder of the molecules that can sometimes be described with a mathematical function. In the diffraction pattern from such a modulated crystal the standard periodic main reflections are flanked by satellite reflections. Generally, incommensurately modulated crystal diffraction cannot be simply described using integers along the reciprocal-lattice directions. However, in the special commensurate case where the satellite spacing is rational relative to the main reflections, a supercell can be used to describe the modulation. Using a supercell allows structural processing to proceed in a `normal' fashion but with the downside of dealing with many more atoms. Not much is known about the relationship between a highly modulated macromolecular crystal and the resulting satellite intensities so in this study a modulated protein crystal was simulated using a supercell approach. The protein superstructure was modulated to varying degrees and the resultant diffraction patterns and electron-density maps were studied to understand better how a modulation may manifest itself in real protein data. In the case that was evaluated, relatively small structural modulation resulted in significant satellite intensities. Interesting cases were observed where extinguished main reflections had strong satellites.