Biomedical subjects

T E Petrova

Publications and source records attributed to T E Petrova.

3 recordsLinked to original sources

PubMed2000

Ab initio low-resolution phasing in crystallography of macromolecules by maximization of likelihood.

Statistical likelihood criteria were tested to select the true (or closest to true) structure-factor phases from an ensemble of phase sets. To define the criterion value for a given trial phase set, the trial 'molecular region' is defined as a region consisting of the points with the highest values in the Fourier synthesis calculated with the observed magnitudes and the trial set of phases. The structure studied is considered as composed of atoms randomly placed inside the trial molecular region. The figure of merit is defined as the likelihood corresponding to this hypothesis, i.e. the probability that the structure-factor magnitudes calculated (from the positions of atoms randomly placed into the trial region) are equal to the observed magnitudes. The concept of generalized likelihood is introduced to make the calculations more straightforward. The tests performed for known structures with the use of experimentally observed magnitudes show that in general it is impossible to unambiguously determine the best phases among a 'population' of trial phase sets. Nevertheless, the random generation of a great number of phase sets and the selection of phase sets with high likelihood values give a collection of variants with a higher concentration of 'good' phase sets than those found in the original population. Averaging the selected phase sets gives a starting solution of the low-resolution phase problem.

Crystallins↗

PubMed2000

Low-resolution ab initio phasing: problems and advances.

If only native amplitudes are used for structure determination, then additional 'theoretical' information is necessary to determine their phases. For use in a phasing procedure, this information can be formulated as a selection criterion (figure of merit) which assigns a reliability weight to every trial phase set and distinguishes the closest ones to the true phase set. Different types of additional information may be tested as a selection criterion: electron-density histograms, connectivity properties, statistical likelihood, atomicity etc. A common feature of such criteria is that they do not unambiguously judge the phase quality at low resolution. Nevertheless, the selection of the phase sets with best criterion values increases the ratio of good phase sets in the ensemble considered. An approximate solution of the phase problem may then be found by averaging the selected phase sets. Cluster analysis of the selected phase sets and averaging within clusters allow further improvement of this solution.

Cluster Analysis↗

PubMed1998

On the ab initio solution of the phase problem or macromolecules at very low resolution. II. Generalized likelihood based approach to cluster discrimination.

The multisolution strategies for direct phasing at very low resolution, such as the few atoms model technique, result in a number of alternative phase sets, each of them arising from a cluster of closely related models. Use of a Monte-Carlo type computer procedure is suggested to choose between the possible phase sets. It consists of generating a large number of pseudo-atom models inside the mask defined by a trial phase set and the use of histograms of magnitude correlation to evaluate the masks. It is shown that the procedure may be considered as a generalization of the statistical maximum-likelihood principle and may be used as a powerful supplementary tool in the likelihood-based approaches to the phase problem solution.

Cluster Analysis↗