On a fast calculation of structure factors at a subatomic resolution

In the last decade, the progress of protein crystallography allowed several protein structures to be solved at a resolution higher than 0.9 Å. Such studies provide researchers with important new information reflecting very fine structural details. The signal from these details is very weak with respect to that corresponding to the whole structure. Its analysis requires high-quality data, which previously were available only for crystals of small molecules, and a high accuracy of calculations. The calculation of structure factors using direct formulae, traditional for `small-molecule' crystallography, allows a relatively simple accuracy control. For macromolecular crystals, diffraction data sets at a subatomic resolution contain hundreds of thousands of reflections, and the number of parameters used to describe the corresponding models may reach the same order. Therefore, the direct way of calculating structure factors becomes very time expensive when applied to large molecules. These problems of high accuracy and computational efficiency require a re-examination of computer tools and algorithms. The calculation of model structure factors through an intermediate generation of an electron density [Sayre (1951). Acta Cryst. 4, 362-367; Ten Eyck (1977). Acta Cryst. A33, 486-492] may be much more computationally efficient, but contains some parameters (grid step, `effective' atom radii etc.) whose influence on the accuracy of the calculation is not straightforward. At the same time, the choice of parameters within safety margins that largely ensure a sufficient accuracy may result in a significant loss of the CPU time, making it close to the time for the direct-formulae calculations. The impact of the different parameters on the computer efficiency of structure-factor calculation is studied. It is shown that an appropriate choice of these parameters allows the structure factors to be obtained with a high accuracy and in a significantly shorter time than that required when using the direct formulae. Practical algorithms for the optimal choice of the parameters are suggested.