Phase improvement and extension

Abstract

The descriptions of the various types of Fourier synthesis (observed, difference, hybrid) and of their properties, given in Chapter 7, suggest that electron density maps are not only a tool for depicting the distribution of the electrons in the target structure, but also a source of information which may be continuously exploited during the phasing process, no matter whether ab initio or non-ab initio methods were used for deriving the initial model. Here, we will describe two important techniques based on the properties of electron density maps. (i) The recursive approach for phase extension and refinement called EDM (electron density modification). Such techniques have dramatically improved the efficiency of phasing procedures, which usually end with a limited percentage of phased reflections and non-negligible phase errors. EDM techniques allow us to extend phase assignment and to improve phase quality. The author is firmly convinced that practical solution of the phase problem for structures with Nasym up to 200 atoms in the asymmetric unit may be jointly ascribed to direct methods and to EDM techniques. (ii) The AMB (automated model building) procedures; these may be considered to be partly EDM techniques and they are used for automatic building of molecular models from electron density maps. Essentially, we will refer to proteins; the procedures used for small to medium-sized molecules have already been described in Section 6.3.5. Two new ab initio phasing approaches, charge flipping and VLD, essentially based on the properties of the Fourier transform, belong to the EDM category, and since they require a special treatment, they will be described later in Chapter 9. Phase extension and refinement may be performed in reciprocal and in direct space. We described the former in Section 6.3.6; here, we are just interested in direct space procedures, the so-called EDM (electron density modification) techniques. Such procedures are based on the following hypothesis: a poor electron density map, ρ, may be modified by a suitable function, f , to obtain a new map, say ρmod, which better approximates the true map: . . . ρmod (r) = f [ρ(r)]. (8.1) . . . If function f is chosen properly, more accurate phases can be obtained by Fourier inversion of ρmod, which may in turn be used to calculate a new electron density map.