An ab initio method is described for solving protein structures for which a
tomic resolution (better than 1.2 Angstrom) data are available. The problem
is divided into two stages. Firstly, a substructure composed of a small pe
rcentage (similar to 5%) of the scattering matter of the unit cell is posit
ioned. This is used to generate a starting set of phases that are slightly
better than random. Secondly, the full structure is developed from this pha
se set. The substructure can be a constellation of atoms that scatter anoma
lously, such as metal or S atoms. Alternatively, a structural fragment such
as an idealized alpha-helix or a motif from some distantly related protein
can be orientated and sometimes positioned by an extensive molecular-repla
cement search, checking the correlation coefficient between observed and ca
lculated structure factors for the highest normalized structure-factor ampl
itudes \E\. The top solutions are further ranked on the correlation coeffic
ient for all E values. The phases generated from such fragments are improve
d using Patterson superposition maps and Sayre-equation refinement carried
out with fast Fourier transforms. Phase refinement is completed using a nov
el density-modification process referred to as dynamic density modification
(DDM). The method is illustrated by the solution of a number of known prot
eins. It has proved fast and very effective, able in these tests to solve p
roteins of up to 5000 atoms. The resulting electron-density maps show the m
ajor part of the structures at atomic resolution and can readily be interpr
eted by automated procedures.