Direct methods in protein crystallography

Abstract

It is pointed out that the 'direct methods' of phase determination for small-structure crystallography do not have immediate applicability to macromolecular structures. The term 'direct methods in macromolecular crystallography' is suggested to categorize a spectrum of approaches to macromolecular structure determination in which the analyses are characterized by the use of two-phase and higher-order-phase invariants. The evaluation of the invariants is generally obtained by the use of heavy-atom techniques. The results of a number of the more recent algebraic and probabilistic studies involving isomorphous replacement and anomalous dispersion thus become valid subjects for discussion here. These studies are described and suggestions are also presented concerning future applicability. Additional discussion concerns the special techniques of filtering, the use of non-crystallographic symmetry, some features of maximum entropy and attempts to apply phase-determining formulas to the refinement of macromolecular structure. It is noted that, in addition to the continuing remarkable progress in macromolecular crystallography based on the traditional applications of isomorphous replacement and anomalous dispersion, recent valuable advances have been made in the application of non-crystallographic symmetry, in particular, to virus structures and in applications of filtering. Good progress has also been reported in the application of exact linear algebra to multiple-wavelength anomalous-dispersion investigations of structures containing anomalous scatterers of only moderate scattering power.

An evolutionary computational approach to the phase problem in macromolecular X-ray crystallography

“…Since no phase information is recorded with these amplitudes, the direct Fourier reconstruction of the crystal structure from its corresponding diffraction pattern is not trivial and other means of deriving this phase information must generally be used (Karle, 1989). This`phase problem' is one of the major and ratelimiting steps in macromolecular X-ray crystallography and generally requires recourse to further experimental methods such as multiple isomorphous replacement (MIR) (Watenpaugh, 1985) or multiwavelength anomalous dispersion (MAD) (Hendrickson et al, 1988) in cases where no suitable structurally homologous model can be found for more direct phasing by molecular replacement (Rossmann & Blow, 1962).…”

The pseudo-atom approach to phase determination in protein electron crystallography – noncentrosymmetric projections. Erratum

“…In recent years, there has been increasing activity, exploring the possibilities of direct determination of crystallographic phases for diffraction data from proteins. Although the large number of atoms in the unit cell can severely limit the application of traditional probabilistic methods (Karle, 1989), there have been alternative approaches (Hauptman, 1993;Miller, DeTitta, Jones, Langs, Weeks & Hauptman, 1993), where a nearly correct phase solution in a multiple set can be identified to lie near a previously identified optimal figure of merit so that these phases can be improved by annealing to determine the correct crystal structure (Weeks, Hauptman, Smith, Blessing, Teeter & Miller, 1995). Thus, given experimental X-ray intensities from a protein (e.og.…”

Ab initio direct methods: practical advice for getting beyond the first 300 atoms

“…The Sayre tangent formula (Woolfson & Yao, 1990) and minimal function (Guo & Hauptman, 1990), discussed in this symposium, appear to have a larger radius of convergence than traditional tangent-formula methods, and it is expected that more structures exceeding 200 atoms will be determined in the near future. Other tangent-formula modifications such as those incorporating higher-order determinants (Karle, 1971;Tsoucaris, 1980) may eventually prove to be more powerful in ab initio macromolecular phasing applications, but, in the words of Jerome Karle (1989), 'These techniques have not achieved widespread use up to this time, presumably because there are alternative techniques that investigators have found to be preferable. ' Entropy-based phasing methods, in comparison, appear to be capable of converging to a solution for much larger structures, say 600 atoms or more (Harrison, 1989;Sj61in, Prince, Svensson & Gilliland, 1991;Sj61in & Prince, 1991;Gilmore, Henderson & Bricogne, 1991), but the success of these procedures has not always been well documented and may require sieving through a large number of trial electron-density maps in order to find one which is capable of producing a solution.…”