Phasing from an envelope.

Solution of the phase problem is central to crystallographic structure determination. Conventional molecular-replacement methods are ineffective in the absence of knowledge of the structure of a homologous protein. A recent method utilizing the low-resolution molecular shape determined from solution X-ray scattering data has been shown to be successful in locating the molecular shape within the crystallographic unit cell for the cases of the trimeric nitrite reductase (AxNiR, 105 kDa) and the dimeric superoxide dismutase (SOD, 32 kDa). This was achieved by performing a direct real-space search for orientation and translation using the orientation of the non-crystallographic axis obtained by performing a self-rotation on the crystallographic data. This effectively reduces the potential six-dimensional search to a four-dimensional one (Eulerian angle gamma and three translational parameters). The program FSEARCH incorporating this method has been generalized to handle molecules from all space groups. The program can also be used in general six-dimensional cases for a molecular-replacement solution given a predetermined envelope from any source, such as electron-microscopic images or solution scattering, provided that the envelope can be converted to the standard CCP4 map format or expressed in terms of spherical harmonics. It is hoped that this method will greatly facilitate the ab initio structure determination of proteins and provide a good foundation for further structure refinement.