High-resolution crystallography and drug design.

Ultra-high-resolution X-ray crystallography of macromolecules (i.e. resolution better than 0.8 Angstroms) is a rising field that promises to provide new insight into the structure-function relationships of biomacromolecules. The picture emerging from macromolecular structures at this resolution is far more complex than previously understood, requiring for its study improved tools for structure refinement, analysis and annotation. Some of these problems were highlighted during the recent High Resolution Drug Design Meeting (Bischenberg-Strasbourg, France, 13-16 May 2004). We will review here some of the results and discussions that took place during that meeting and elaborate on the trends and challenges ahead in this emerging new field of research.

Low-resolution data analysis for low-density lipoprotein particle.

The knowledge of the molecular structure of LDL, a large lipoprotein complex, is of great interest for medical investigations. Currently available LDL crystals do not diffract to high resolution and do not allow the application of standard crystallographic techniques. Additional difficulties arise because of a very dense crystal packing and the presence of several components with quite different mean densities. Several ab initio phasing methods previously reported by the authors have been successfully applied to find a crystallographic image of LDL at a resolution of 27 A. The most promising results have been obtained using direct phasing with a connectivity analysis of the electron-density maps. The current image makes it possible to discern a single particle covered by a layer of relatively high density that is asymmetrically distributed on the particle surface. It shows a partition of high and low densities inside the particle and, in particular, strips of varying density in the lipid core.

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.

Density constraints and low-resolution phasing.

Direct phasing needs additional information of a non-specific kind in order to select the correct phase set from all possible ones. This paper analyses the use of constraints which can be formulated in terms of electron-density values. One- and multi-dimensional histograms and connectivity properties are implemented as such constraints in density-modification procedures. These approaches usually cannot unambiguously select the best solution from a set of alternative phase variants. Nevertheless, they do allow the rejection of wrong solutions and the use of cluster analysis and averaging on the remaining variants provide a good starting point for further phase-refinement procedures.

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.

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.

A multicopy modeling of the water distribution in macromolecular crystals.

A multicopy protocol is proposed for modeling macromolecular hydration using diffraction experimental data (X-ray or neutron) to search for a better description of delocalized water sites than that given by point water models. The model consists of one macro-molecule and several copies of each water molecule, refined simultaneously against diffraction data using molecular dynamics techniques. The protocol was applied to BPTI and an RNA tetradecamer. The sites defined by the different copies range from very ordered ones to continuous channels; they fit the density maps and agree with the diffraction amplitudes with an accuracy comparable with usual crystallographic methods. The delocalization of water in channels agrees with the high mobility observed in NMR experiments.

Approaches to very low resolution phasing of the ribosome 50S particle from Thermus thermophilus by the few-atoms-models and molecular-replacement methods.

Estimates for the phases of the X-ray diffraction data from the 50S ribosomal particle of Thermus thermophilus has been made to an effective resolution around 80 A using the few-atoms-modes ab initio technique [Lunin, Lunina, Petrova, Vernoslova, Urzhumtsev & Podjarny (1995). Acta Cryst. D51, 896-903]. This technique models the density with a small number of Gaussian spheres to generate a large number of possible phase sets and then uses clustering algorithms to identify the best ones. Independently, an envelope obtained from electron-micrograph image reconstruction [Yonath, Leonard & Wittmann (1987). Science, 236, 813-816] was oriented and positioned using the molecular-replacement technique, specially adapted to the very low resolution case [Urzhumtsev & Podjarny (1995). Acta Cryst. D51, 888-895]. The two methods show similar packing arrangements. The electron density calculated by the few-atoms-models technique without any assumption on the number of molecules in asymmetric unit or on their shape shows recognizable features of the particle.

On the ab initio solution of the phase problem for macromolecules at very low resolution: the few atoms model method.

A method is proposed for the solution of the phase problem at very low resolution for macromolecules. It generates randomly a very large number of models, each consisting of a few (two to ten) pseudo-atoms. The corresponding amplitudes are used for selecting a subset of 'best' models by choosing those with the highest correlation with experimental values. The phases calculated from these 'best' models are analysed by a clusterization procedure leading to a few possible solutions, from which the correct one can be recognized by simple additional criteria. This method has been successfully applied to the neutron diffraction data of the AspRS-tRNA(Asp) complex at 50 A resolution and to data calculated from a model ribosome crystal at 60 A resolution.

Heavy-atom refinement against solvent-flattened phases.

A new algorithm for refinement of heavy-atom parameters is defined by an iterative procedure where external phases are provided by density modification. This algorithm is applied to two cases, tRNA(Asp) and the complex between tRNA(Asp) and aspartyl-tRNA synthetase. In the first case, where the structure was solved by multiple isomorphous replacement (MIR) methods, it was found that the new method gives accurate values for the native-derivative scale and four occupancy of heavy-atom sites. Position refinement was more delicate and it needed to be handled in a restricted resolution range. In the second case, where a similar method was used in the early stages of solving the phase problem, it slightly decreased the phase error. It was followed by an improvement of the density-modification masks, which led to better maps at higher resolution.

Crystal structure of the nucleosome core particle at 16 A resolution.

The crystal structure of the nucleosome core particle has been studied by neutron diffraction to a resolution of 16 A. By using H2O/D2O solvent contrast variation, the structures of the DNA and histone core were analysed separately. The DNA, as seen at this resolution, forms a super-helix of pitch 25.8 A, radius 42.1 A and 1.8 turns in length. The histone core itself is approximately helical and follows the DNA along the inside of the super-helix, giving the nucleosome core particle an overall 2-fold axis of symmetry. Four regions can be distinguished in the protein density, which we interpret as dimers of histones within the octameric core. The dimers have been assigned on the basis of other evidence as being of two kinds, (H2A-H2B) and (H3-H4). Because solvent contrast variation can distinguish between hydrophobic and hydrophilic regions in the protein density, our results suggest that the interface between the monomers of each dimer is probably quite hydrophobic in character, while the interaction between dimers is weaker and/or more hydrophilic. The protein is in contact with most of the DNA and there are some regions where it may penetrate between the turns of the super-helix. In particular, the tetramer (H4-H3)-(H3-H4) is in close contact with the central part of the DNA, but significant contacts are seen also between the histones H3 and the extremities of the super-helix, thus explaining the stability of a nucleosome-like particle depleted of H2A and H2B. Significant departures from the molecular 2-fold axis of symmetry occur in the relative arrangements of the two (H2A-H2B) dimers.