Crystallographic Aspects of Protein Phasing at Very Low Resolution

Sammanfattning: A protein crystallographic method for obtaining structure factor phases of low-order reflections is presented. It is based on four observations: 1) The electron density inside proteins is relatively smooth and uniform at low resolution. 2) Since all proteins have almost the same density, the total volume of the protein is known if the molecular weight is known. 3) Many proteins are fairly spherically shaped or may be at least be approximated as spheres at very low resolution. 4) The total scattering from a globular protein of uniform density is in phase with a point scatterer at its centre of gravity, up to a well-defined cross-over. After the first cross-over the total protein molecule scatters out of phase with its centre. The centre of the protein can be found using a translation algorithm in which the spherical interference function acts as a search model. Small errors in the position (Dr»5Å) do not severely affect phases of the typically ten lowest resolution reflections.The method works, provided low-order reflections can be accurately measured and the centre of gravity can be well positioned from these data. The correctly phased low resolution reflections may be used as a starting set for phase extension. By combining the measured amplitudes with these phases the size and low-resolution shape of an unknown protein i.e. the envelope of the molecule might be obtained.