Ab initio phasing using molecular envelope from solution X-ray scattering

Solving the phase problem is the crucial and quite often the most difficult and time-consuming step in crystallographic structure determination. The traditional methods of isomorphous replacement (MIR or SIR) and molecular replacement require the availability of an isomorphous heavy-atom derivative or the structure of a homologous protein, respectively. Here, a method is presented which utilizes the low-resolution molecular shape determined from solution X-­ray scattering data for the molecular search. The molecular shape of a protein is an important structural property and can be determined directly by the small-angle scattering ­technique. The idea of locating this molecular shape in the crystallographic unit cell has been tested with experimental diffraction data from nitrite reductase (NiR). The conventional Patterson search proved to be unsuccessful, as the intra-envelope vectors are uniformly distributed and do not match those of intra-molecular (atom-to-atom) vectors. A direct real-space search for orientation and translation was then performed. A self-rotation function using 2.8 Å crystallographic data yielded the polar angles of the non-crystallographic threefold axis. Knowledge of the orientation of this axis reduces the potential six-dimensional search to four (Eulerian angle γ and three translational parameters). The direct four-dimensional search within the unit cell produced a clear solution. The electron-density map based on this solution agrees well with the known structure, and the phase error calculated from the map was 61° within 20 Å resolution. It is anticipated that the low-resolution envelope can be used as a starting model for phase extension by the maximum-entropy and density-modification method.