Direct phase determination of large macromolecular crystals using three-beam x-ray interference

Phase determination of X-ray reflections in a quasicrystal

“…A general review of multibeam literature was published a few years ago (Chang, 1987) and recently phase effects have been observed in protein crystals (Hiimmer, Schwegle & Weckert, 1991;Chang, King, Huang & Gao, 1991).…”

Enantiomorphism and multiple-beam X-ray diffraction

“…In view of the analysis given in this paper, the results presented by Chang, King, Huang & Gao (1991) and by Hiimmer, Weckert & Bondza (1989) are somewhat questionable. This work was supported by the National Science Foundation, grant no.…”

“…Another case in point is the paper by Chang, King, Huang & Gao (1991), in which some multi-beam experiments on large macromolecular crystals are described. It is mentioned in the Abstract of this paper that 'the crystal polarity (enantiomorph) is determined unambiguously from the peak intensity measurement'.…”

Quantitative phase determination for macromolecular crystals using stereoscopic multibeam imaging

“…This modi®cation on the G or L diffracted beam is thus related to the phases of the G, L and GÀL re¯ections or, more precisely, the triplet phases 3 ( ÀG L GÀL ) or 3 ( ÀL G LÀG ) of the structure-factor triplets F ÀG F L F GÀL or F ÀL F G F LÀG , respectively, provided that the anomalous dispersion is negligibly small (Chang, 1987, and references therein; Weckert & Hu È mmer, 1997, and references therein). For macromolecular crystals, the three-beam (O, ÀG, ÀL) case needs to be used together with the (O, G, L) case to determine their enantiomorphs (Hu È mmer et al, 1991;Chang et al, 1991). Usually, the multiple diffraction pro®les, the intensity I G versus the rotation angle É, of the G re¯ection are recorded one at a time with a point detector like a scintillation counter (Chang, 1987, and references therein; Weckert & Hu È mmer, 1997, and references therein).…”

“…Although the existing mathematical methods, such as direct methods (Ladd & Palmer, 1980;Schenk, 1991;Woolfson & Fan, 1995), multiwavelength anomalous scattering (MAD) (Hendrickson, 1991), and many others (Rossmann, 1972;Bricogne & Gilmore, 1990) are useful phasing techniques for small and macromolecular crystals, the phase problem is not yet completely solved because direct methods run into dif®culties with macromolecules since the probability of having the correct phase relation is inversely related to the number of atoms in the crystal unit cell (Ladd & Palmer, 1980) and suitable wavelengths and heavy-atom derivatives may not always be obtainable. Recently, multiple diffraction techniques utilizing interference effects (Post, 1977;Chapman et al, 1981;Chang, 1982;Juretschke, 1982;Hoier & Aanestad, 1981;Hu È mmer & Billy, 1986;Chang, 1987, and references therein; Mo et al, 1988;Shen & Finkelstein, 1990) have demonstrated their capability of physically measuring re¯ection phases qualitatively and quantitatively (Chang & Tang, 1988;Weckert & Hu È mmer, 1990) without invoking multiwavelength experiments and heavy-atom derivatives for macromolecular crystals (Hu È mmer et al, 1991;Chang et al, 1991;Weckert & Hu È mmer, 1997, and references therein). Unfortunately, the intensity pro®les of multiple diffraction used in phase determination are usually obtained one at a time.…”