A study of the accurate electron-density distribution in molecular crystals at subatomic resolution (better than $1.0 Å ) requires more detailed models than those based on independent spherical atoms. A tool that is conventionally used in small-molecule crystallography is the multipolar model. Even at upper resolution limits of 0.8-1.0 Å , the number of experimental data is insufficient for full multipolar model refinement. As an alternative, a simpler model composed of conventional independent spherical atoms augmented by additional scatterers to model bonding effects has been proposed. Refinement of these mixed models for several benchmark data sets gave results that were comparable in quality with the results of multipolar refinement and superior to those for conventional models. Applications to several data sets of both small molecules and macromolecules are shown. These refinements were performed using the general-purpose macromolecular refinement module phenix.refine of the PHENIX package.

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In the last decade, high-resolution data have become available for macromolecular objects. Furthermore, ultrahigh-resolution diffraction data (resolution close to 0.6 A) have been collected for several protein crystals. This allows the study of fine details of the electron-density distribution such as the deformation density, i.e. the deviation of the experimentally determined electron density from the density composed of 'free' non-bonded atoms. This paper discusses the resolution and atomic temperature factors necessary to make the valence electron density visible at individual bonds in conventional difference maps for macromolecules. The study of theoretical maps calculated by quantum-chemistry methods allows estimation of these conditions; these results are confirmed by analysis of experimental maps for Leu-enkephalin and antifreeze protein RD1. A resolution limit close to 0.6 A was found to be highly important for refinement even when the maps were calculated at lower resolution. The refinement of the same models at near to 0.9 A resolution results in artificially increased values of the atomic displacement parameters and does not permit bond electron density to be visible in difference maps. To some extent, overestimation of the atomic displacement parameters may be restricted if dummy bond electrons are used in the refinement.

The three-dimensional crystal structure of Serratia marcescens endonuclease has been refined at 1.1 A resolution to an R factor of 12.9% and an R(free) of 15.6% with the use of anisotropic temperature factors. The model contains 3694 non-H atoms, 715 water molecules, four sulfate ions and two Mg(2+)-binding sites at the active sites of the homodimeric protein. It is shown that the magnesium ion linked to the active-site Asn119 of each monomer is surrounded by five water molecules and shows an octahedral coordination geometry. The temperature factors for the bound Mg(2+) ions in the A and B subunits are 7.08 and 4.60 A(2), respectively, and the average temperature factors for the surrounding water molecules are 12.13 and 10.3 A(2), respectively. In comparison with earlier structures, alternative side-chain conformations are defined for 51 residues of the dimer, including the essential active-site residue Arg57. A plausible mechanism of enzyme function is proposed based on the high-resolution S. marcescens nuclease structure, the functional characteristics of the natural and mutational forms of the enzyme and consideration of its structural analogy with homing endo-nuclease I-PpoI.

Reasonable assumptions about the statistical properties of errors in an atomic model lead to the probability distributions for the values of structure-factor phases. These distributions contain some generally unknown parameters reflecting how large the model errors are. These parameters must be determined properly to give realistic estimates of phase errors. Maximum-likelihoodbased estimates suggested by Lunin & Urzhumtsev [Acta Cryst. (1984), A40, 269-277] are good for models not subjected to refinement but underestimate the errors when being used for ref'med models. The R-free methodology of Brianger [Nature (London), (1992), 355,472-474] applied to the likelihood-function calculation allows realistic phase-error estimates to be obtained for both unrefined and refined models. These estimates may be used as an additional indicator in the refinement process.