Confined structures: basic crystallographic aspects

Abstract

The concept of a con®ned structure is introduced. The statistical properties of the structure factors for such structures are derived and the main features of the Patterson function are described. It is shown that the structure-factor distributions for the con®ned structures coincide with those derived for the rational index re¯ections of ordinary structures. Algorithms potentially useful for protein crystal structure solution are identi®ed and checked via experimental applications.

Reconstruction of complex single-particle images using charge-flipping algorithm

“…The object and diffraction pattern are assumed to be related by simple Fourier transform, and no multiple scattering or Ewald sphere curvature effects are considered. Recently, the reconstruction of non-periodic structures by diffractive imaging has stimulated considerable interest as a contribution to new methods for solving protein structures that cannot be crystallized (Spence & Doak, 2004;Miao et al, 1999;Miao & Sayre, 2000;De Caro et al, 2002;He et al, 2003). The first successful application of diffractive imaging to electron diffraction data was reported by Weierstall et al (2001) and it has been used more recently to produce the first atomic resolution image of a single carbon nanotube (Zuo et al, 2003).…”

Phasing diffuse scattering. Application of theSIR2002algorithm to the non-crystallographic phase problem

“…The phase problem for non-periodic objects (Stark, 1987) has been studied by many different approaches, some of which have recently demonstrated striking success with experimental data: a. the Gerchberg-Saxton-Fienup HIO algorithm (Fienup, 1982(Fienup, , 1987Miao et al, 1999Miao et al, , 2002, who refer the method as oversampling; see also De Caro et al, 2002 who refer to it by using the concept of confined structure);…”