Phasing proteins at low resolution

A method for obtaining phases of low-order reflections is presented. It is based on four observations: (1) the electron density inside proteins is 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) The overall shape of many proteins is fairly spherical. (4) The total scattering from a sphere 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. If the centre of the protein can be found, the phases of typically the ten lowest resolution reflections can be very accurately determined. The method works, provided low-order reflections can be measured accurately 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 we believe that the size and low-resolution shape of an unknown protein, i.e. the envelope of the molecule, can be obtained.