Biomedical subjects

Hongliang Xu

Publications and source records attributed to Hongliang Xu.

6 recordsLinked to original sources

PubMed2006

Recent advances in direct phasing methods for heavy-atom substructure determination.

Macromolecular crystal structure determination has typically been a two-step process. When diffraction data from multiple chemically isomorphous or anomalously scattering crystals are available, the positions of heavy atoms from amplitude differences arising from native-derivative crystal pairs or an anomalously scattering crystal are first located and phasing of the whole protein structure is then completed using the heavy-atom substructure as a bootstrap. Shake-and-Bake, a direct-methods-based dual-space refinement procedure, provides heavy-atom substructure solutions by finding the constrained global minimum of a probabilistically defined minimal function. This minimal function relies on probabilistic estimates of the cosines of the structure invariants. A novel statistically defined minimal function that utilizes the statistical properties of the structure invariants has recently been proposed and tested. Applications of the statistical Shake-and-Bake procedure show that statistical direct methods provide a simple, reliable and efficient method of heavy-atom substructure determination.

Crystallography, X-Ray↗

PubMed2005

Optimizing statistical Shake-and-Bake for Se-atom substructure determination.

A novel statistical approach to the phase problem in X-ray crystallography was introduced in a recent paper [Xu & Hauptman (2004), Acta Cryst. A60, 153-157]. In this approach, a new minimal function based on the statistical distribution of structure-invariant values serves as the foundation of an optimization procedure called statistical Shake-and-Bake. Favorable application of this procedure to Se-atom substructure determination depends on the choice of the statistical interval over which the function is defined. The effects of interval variation have been studied for 19 Se-atom substructures ranging in size from five to 70 Se atoms in the asymmetric unit and the results have shown an overall improvement in success rate relative to traditional Shake-and-Bake. Statistical Shake-and-Bake is being incorporated as the default optimization procedure in newly distributed versions of the SnB and BnP computer programs.

Crystallography, X-Ray↗

PubMed2004

Statistical approach to the phase problem.

The minimal function and its minimal principle employed in the traditional Shake-and-Bake algorithm rely on the probabilistic estimates of the cosines of the structure invariants. In this paper, a novel statistical approach to the phase problem, which utilizes statistical properties of the structure invariants, is proposed. The statistical maximal function and its maximal principle are formulated, and the corresponding statistical Shake-and-Bake algorithm and its associated statistical parameter-shift procedure are proposed and tested. The test results show that the statistical approach to the phase problem is a simple, reliable, less computationally intensive and more efficient procedure for phase determination in X-ray crystallography.

Crystallography, X-Ray↗

PubMed2002

On integrating the techniques of direct methods and SIRAS: the probabilistic theory of doublets and its applications.

The mathematical formalism of direct methods is here applied to the SIRAS (single-isomorphous replacement combined with anomalous scattering) case. Specifically, the joint probability distribution of three structure factors, which plays the central role in the probabilistic theory of the two-phase structure invariants (doublets), is derived. This distribution leads directly to the conditional probability distribution of the two-phase structure invariants, given the values of selected sets of magnitudes. Furthermore, a probabilistic formula for estimating individual phases of the derivative structure is derived, provided that the heavy-atom substructure is assumed to be known. The formulas were tested for experimental SIRAS data and results are reported.

Acetylesterase↗

PubMed2002

Algebraic direct methods for few-atoms structure models.

As a basis for direct-methods phasing at very low resolution for macromolecular crystal structures, normalized structure-factor algebra is presented for few-atoms structure models with N = 1, 2, 3, em leader equal atoms or polyatomic globs per unit cell. Main results include: [see text]. Triplet discriminant Delta(hk) and triplet weight W(hk) parameters, a approximately 4.0 and b approximately 3.0, respectively, were determined empirically in numerical error analyses. Tests with phases calculated for few-atoms 'super-glob' models of the protein apo-D-glyceraldehyde-3-phosphate dehydrogenase (approximately 10000 non-H atoms) showed that low-resolution phases from the new few-atoms tangent formula were much better than conventional tangent formula phases for N = 2 and 3; phases from the two formulae were essentially the same for N > or = 4.

Crystallization↗

PubMed2001

Sine-enhanced Shake-and-Bake: the theoretical basis and applications to Se-atom substructures.

Shake-and-Bake is a dual-space direct-methods procedure for crystal structure determination capable of providing ab initio solutions for structures containing as many as 1200 independent non-H atoms, as well as for heavy-atom substructures containing as many as 160 Se atoms in the asymmetric unit. In traditional Shake-and-Bake, phase refinement in reciprocal space utilizes the technique of parameter shift to reduce the value of a minimal function that considers only the mean-square differences between the current values of the cosine structure invariants and their expected values. A new type of minimal function, termed the sine-enhanced minimal function, considers both cosine and sine values of the structure invariants. Exhaustive tests on six Se-atom substructures, ranging in size from 12 to 160 Se atoms in the asymmetric unit, have shown that a two- to eightfold increase in the percentage of trials that converge to solution is attainable with the technique of sine-enhanced parameter shift. The corresponding sine-enhanced Shake-and-Bake, with suitable default parameter values, is being incorporated into a new distributed version of the SnB computer program.

Crystallography, X-Ray↗