N. L. Lunina

Seminvariant density decomposition and connectivity analysis and their application to very low resolution macromolecular phasing.

A low-resolution Fourier synthesis is thought to show a molecule as a compact region of a high electron density. As a consequence, the number of such regions, chosen at a proper cut-off level, should be equal to the number of molecules in the unit cell. This hypothesis may be used as a basis for selection criteria in multisolution ab initio phasing procedures. However, when working with a small number of reflections, this hypothesis may break down. The suggested Fourier-synthesis decomposition explains some reasons for failure and provides a connectivity-based procedure for the determination of macromolecular position in the crystal unit cell and the phasing of several low-resolution reflections. The simplest decomposition consists in separating the reflections into two sets according to whether their phases do or do not depend on a permitted origin shift. It is shown that the partial Fourier syntheses corresponding to these subsets are simply a half-sum and a half-difference of the initial electron-density distribution with its shifted copy. Therefore, they display the true images overlapped with the shifted ones (or with shifted and additionally flipped copies for the latter synthesis). The paper generalizes the decomposition for the case of a finite subgroup of the group of permitted origin shifts and reveals the role of one-phase sem-invariants.

On the Ab Initio Solution of the Phase Problem for 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.

Ab initio phasing starting from low resolution

A single set of structure factor magnitudes complete at low resolution plus information of a general type are sufficient to get initial phases for macromolecular crystals which allow one to see the molecular packing and an approximate envelope. Followed by a more careful analysis based on the same information, these ab initio phases can be extended so that the corresponding maps show secondary structure elements.

New possibilities of X-ray nanocrystallography of biological macromolecules based on X-ray free-electron lasers

X-ray serial nanocrystallography is a new technique for determining the three-dimensional structure of biological macromolecules from data on the diffraction of ultrashort pulses generated by X-ray free-electron lasers. The maximum achievable resolution for a set of experimental data as a function of the sample sizes and parameters of the equipment is estimated based on simulations of the diffraction process with allowance for changes in the electronic structure of the atoms of the sample under the influence of X-rays. Estimates show that nanocrystallography greatly enhances the possibilities of X-ray analysis, reducing the requirements for the minimum permitted size of the crystals and enabling to explore poorly crystallizable molecular objects, such as many membrane proteins and complexes of macromolecules.