Bulk-solvent and overall scaling revisited: faster calculations, improved results. Corrigendum

Equations in Sections 2.3 and 2.4 of the article by Afonine et al. [Acta Cryst. (2013). D69, 625-634] are corrected.

Efficient structure-factor modeling for crystals with multiple components

Diffraction intensities from a crystallographic experiment include contributions from the entire unit cell of the crystal: the macromolecule, the solvent around it and eventually other compounds. These contributions cannot typically be well described by an atomic model alone, i.e. using point scatterers. Indeed, entities such as disordered (bulk) solvent, semi-ordered solvent (e.g. lipid belts in membrane proteins, ligands, ion channels) and disordered polymer loops require other types of modeling than a collection of individual atoms. This results in the model structure factors containing multiple contributions. Most macromolecular applications assume two-component structure factors: one component arising from the atomic model and the second one describing the bulk solvent. A more accurate and detailed modeling of the disordered regions of the crystal will naturally require more than two components in the structure factors, which presents algorithmic and computational challenges. Here an efficient solution of this problem is proposed. All algorithms described in this work have been implemented in the computational crystallography toolbox (CCTBX) and are also available within Phenix software. These algorithms are rather general and do not use any assumptions about molecule type or size nor about those of its components.

Polder maps: improving OMIT maps by excluding bulk solvent

The crystallographic maps that are routinely used during the structure-solution workflow are almost always model-biased because model information is used for their calculation. As these maps are also used to validate the atomic models that result from model building and refinement, this constitutes an immediate problem: anything added to the model will manifest itself in the map and thus hinder the validation. OMIT maps are a common tool to verify the presence of atoms in the model. The simplest way to compute an OMIT map is to exclude the atoms in question from the structure, update the corresponding structure factors and compute a residual map. It is then expected that if these atoms are present in the crystal structure, the electron density for the omitted atoms will be seen as positive features in this map. This, however, is complicated by the flat bulk-solvent model which is almost universally used in modern crystallographic refinement programs. This model postulates constant electron density at any voxel of the unit-cell volume that is not occupied by the atomic model. Consequently, if the density arising from the omitted atoms is weak then the bulk-solvent model may obscure it further. A possible solution to this problem is to prevent bulk solvent from entering the selected OMIT regions, which may improve the interpretative power of residual maps. This approach is called a polder (OMIT) map. Polder OMIT maps can be particularly useful for displaying weak densities of ligands, solvent molecules, side chains, alternative conformations and residues both in terminal regions and in loops. The tools described in this manuscript have been implemented and are available in PHENIX.

The solvent component of macromolecular crystals

The mother liquor from which a biomolecular crystal is grown will contain water, buffer molecules, native ligands and cofactors, crystallization precipitants and additives, various metal ions, and often small-molecule ligands or inhibitors. On average, about half the volume of a biomolecular crystal consists of this mother liquor, whose components form the disordered bulk solvent. Its scattering contributions can be exploited in initial phasing and must be included in crystal structure refinement as a bulk-solvent model. Concomitantly, distinct electron density originating from ordered solvent components must be correctly identified and represented as part of the atomic crystal structure model. Herein, are reviewed (i) probabilistic bulk-solvent content estimates, (ii) the use of bulk-solvent density modification in phase improvement, (iii) bulk-solvent models and refinement of bulk-solvent contributions and (iv) modelling and validation of ordered solvent constituents. A brief summary is provided of current tools for bulk-solvent analysis and refinement, as well as of modelling, refinement and analysis of ordered solvent components, including small-molecule ligands.

Bulk-solvent and overall scaling revisited: faster calculations, improved results

A fast and robust method for determining the parameters for a flat (mask-based) bulk-solvent model and overall scaling in macromolecular crystallographic structure refinement and other related calculations is described. This method uses analytical expressions for the determination of optimal values for various scale factors. The new approach was tested using nearly all entries in the PDB for which experimental structure factors are available. In general, the resulting R factors are improved compared with previously implemented approaches. In addition, the new procedure is two orders of magnitude faster, which has a significant impact on the overall runtime of refinement and other applications. An alternative function is also proposed for scaling the bulk-solvent model and it is shown that it outperforms the conventional exponential function. Similarly, alternative methods are presented for anisotropic scaling and their performance is analyzed. All methods are implemented in the Computational Crystallography Toolbox (cctbx) and are used in PHENIX programs.