A real-space refinement procedure for proteins

Abstract

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 ~ (0o-Om)Zdv where Oo is the observed electron density and 0,~ is a density associated with a model in terms of which the observed densities are interpreted. 0,~ 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.aUowed 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 (0o-Ore) 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/~ resolution, but is not limited to this range. It has produced convergent shifts exceeding 1"5 ~ in a map of 2 A resolution, and, except for shifts exceeding 1 A, convergence is essentially complete in one pass. The procedure has, so far, been applied to four proteins. A, B a t all B C

Real-space refinement in Phenix for cryo-EM and crystallography

“…Diamond, 1971;Lunin & Urzhumtsev, 1984;Chapman, 1995;Mooij et al, 2006;Sorzano et al, 2015). While this is much faster than the previous method, it may be less accurate and still be computationally expensive, especially for large models.…”

“…1 It is a widely known consequence of Parseval's theorem (see for example, Diamond, 1971, or Arnold & Rossmann, 1988) that this is equivalent to a least--squares target between a full set of the corresponding complex Fourier coefficients; CNS (Brunger et al, 1998) describes this as a "vector LS target".…”

“…For (2) we suppose that the original target map is optimally scaled to the model map (Diamond, 1971;Chapman 1995). In the following, we will consider the target to be essentially unchanged by manipulations that shift its value by a constant or a scale factor, as such manipulations do not change the position of the minimum of the target.…”

“…"# and model--calculated !"#! maps are provided on the same grid, a continuous integration in (2) and (3) can be replaced with a numeric integration over the regular grid on which the maps are available (see, for example, Diamond, 1971),…”

A group refinement procedure in protein crystallography using Fourier transforms

“…Several well established refinement procedures exist in which the model is constrained or restrained to a geometry known from accurate smallmolecule structures (Diamond, 1971;Jack & Levitt, 1978;Hendrickson & Konnert, 1981). The relative merits of these procedures have been discussed (Deisenhofer, Remington & Steigemann, 1984;Steigemann, 1980).…”