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Biomedical subjects

H Hauptman

Publications and source records attributed to H Hauptman.

8 recordsLinked to original sources
PubMed1997

Phasing methods for protein crystallography.

The phase problem has been formulated as one of constrained global minimization and it leads to the minimal principle, which is the theoretical basis of 'Shake-and-Bake'--an algorithm for the automatic solution of the phase problem, ab initio. A related approach (termed 'Half-Baked') that, as in Shake-and-Bake, alternates phase refinement in reciprocal space with density modification in real space, has recently been formulated. The traditional techniques of direct methods have been integrated with isomorphous replacement and anomalous scattering and the first applications have been made. The accurate measurement of a limited number of structure invariants by means of multiple beam X-ray diffraction has become a reality. A feasibility study shows that, in combination with the direct method, the ability to measure the values of the structure invariants experimentally will strengthen existing techniques.

Algorithms↗
PubMed1993

Phasing macromolecular structures via structure-invariant algebra.

Owing to the breakdown of Friedel's law when anomalous scatterers are present, unique values of the three-phase structure invariants in the whole range from 0 to 2pi are determined by measured values of diffraction intensities alone. Two methods are described for going from presumed known values of these invariants to the values of the individual phases. The first, dependent on a scheme for resolving the 2pi ambiguity in the estimate omega(HK) of the triplet phi(H) + phi(K) + phi(-H-K), solves by least squares the resulting redundant system of linear equations phi(H) + phi(K) + phi(-H-K) = omega(HK). The second attempts to minimize the weighted sum of squares of differences between the true values of the cosine and sine invariants and their estimates. The latter method is closely related to one based on the 'minimal principle' which determines the values of a large set of phases as the constrained global minimum of a function of all the phases in the set. Both methods work in the sense that they yield values of the individual phases substantially better than the values of the initial estimates of the triplets. However, the second method proves to be superior to the first but requires, in addition to estimates of the triplets, initial estimates of the values of the individual phases.

Journal Article↗
PubMed1979

Probabilistic theory of the three-phase structure seminvariant in the space group P1.

By embedding the three-phase structure seminvariant T and its symmetry-related variants in suitable quintets Q, one obtains the extensions Q of the seminvariant T. Because of the space group-dependent relationships among the phases, T is simply related to its extensions Q. In this way the probabilistic theory of the seminvariant T is reduced to that of the quintets Q, which is well developed. In particular, the neighborhoods of T are defined in terms of the neighborhoods of the Qs. The conditional probability distribution of the structure seminvariant T, given the seven magnitudes in its first neighborhood, is described for the space group P1. The distribution yields a reliable estimate (0 or pi) for T in the favorable case that the variance of the distribution happens to be small.

Journal Article↗
PubMed1972

Valinomycin crystal structure determination by direct methods.

The conformation of an uncomplexed form of the antibiotic valinomycin (C(54)N(6)O(18)H(90)) has been determined by direct methods including a novel technique for strong enantiomorph discrimination via the calculation and systematic analysis of cosine invariants of a special type. The intramolecular hydrogen bonding scheme and the isopropyl group stereochemistry of uncomplexed valinomycin are compatible with interpretations of spectral measurements for the complexed and uncomplexed molecule in solution but are different from any previously proposed structure. The simple conformational change of a hydrogen bond shift, which could be induced by the process of potassium ion complexing, transforms the uncomplexed into the complexed structure.

Anti-Bacterial Agents↗