Iterative projection algorithms for ab initio phasing in virus crystallography.

Iterative projection algorithms are proposed as a tool for ab initio phasing in virus crystallography. The good global convergence properties of these algorithms, coupled with the spherical shape and high structural redundancy of icosahedral viruses, allows high resolution phases to be determined with no initial phase information. This approach is demonstrated by determining the electron density of a virus crystal with 5-fold non-crystallographic symmetry, starting with only a spherical shell envelope. The electron density obtained is sufficiently accurate for model building. The results indicate that iterative projection algorithms should be routinely applicable in virus crystallography, without the need for ancillary phase information.

Iterative projection algorithms in protein crystallography. II. Application.

Iterative projection algorithms (IPAs) are a promising tool for protein crystallographic phase determination. Although related to traditional density-modification algorithms, IPAs have better convergence properties, and, as a result, can effectively overcome the phase problem given modest levels of structural redundancy. This is illustrated by applying IPAs to determine the electron densities of two protein crystals with fourfold non-crystallographic symmetry, starting with only the experimental diffraction amplitudes, a low-resolution molecular envelope and the position of the non-crystallographic axes. The algorithm returns electron densities that are sufficiently accurate for model building, allowing automated recovery of the known structures. This study indicates that IPAs should find routine application in protein crystallography, being capable of reconstructing electron densities starting with very little initial phase information.