Ab initio phase determination and phase extension using non-crystallographic symmetry

Non-crystallographic symmetry (NCS) can be used to improve, extend or find ab initio phases to be associated with a set of observed structure amplitudes, resulting in an interpretable electron-density map. The simplest application is merely to improve the accuracy of the phases by cyclically averaging the electron density, Fourier back-transformation of the modified map, and recomputing a new map with the newly found phases. The first sophistication of this procedure is to phase extend, in successive small steps, the currently available phase information to higher resolution, where only observed amplitudes were previously available. A further sophistication is to initiate the phase extension from very low resolution where a simple geometric model, or an electron microscope image, would be consistent with the chosen resolution. A number of recent examples of virus structure determination exist where such ab initio phasing was successful. The ultimate ab initio phase determination would be to extend phases given only an estimate of the F(000) term.