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This paper describes a procedure which optimizes the fitting of a `model' of a protein to an electron density map. The technique seeks to minimize ∫ (QoQm)2dv where Qo is the observed electron density and Qm is a density associated with a model in terms of which the observed densities are interpreted. Qm consists of a Gaussian density centred on each atomic centre, and a floating background level. Interactions due to overlapping densities of neighbouring atoms are allowed for and the model is normally treated as a flexible chain so that bond lengths are conserved during movement. Alternatively, the atoms may be allowed to move independently. Site occupations and atomic radii are also refinable. The calculation is organized in terms of a `molten zone' of up to ten residues, which moves along the chain one residue at a time, linear or non-linear constraints being applied to preserve chain continuity at each end of the zone. Provision is made for the zone to become active or inactive in predetermined regions of the molecule. A difference map (QoQm) is available at the end of the calculation, as is a molecular listing with revised coordinates and dihedral and inter-bond angles. Inter-bond angles may be treated either as constants or as variables, and if variable may be made elastically stiffer than dihedral angles. The procedure is well suited to maps of 2 to 3 Å resolution, but is not limited to this range. It has produced convergent shifts exceeding 1.5 Å in a map of 2 Å resolution, and, except for shifts exceeding 1 Å, convergence is essentially complete in one pass. The procedure has, so far, been applied to four proteins.
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