On the use of logarithmic scales for analysis of diffraction data

Predictions of the possible model parameterization and of the values of model characteristics such as R factors are important for macromolecular refinement and validation protocols. One of the key parameters defining these and other values is the resolution of the experimentally measured diffraction data. The higher the resolution, the larger the number of diffraction data N(ref), the larger its ratio to the number N(at) of non-H atoms, the more parameters per atom can be used for modelling and the more precise and detailed a model can be obtained. The ratio N(ref)/N(at) was calculated for models deposited in the Protein Data Bank as a function of the resolution at which the structures were reported. The most frequent values for this distribution depend essentially linearly on resolution when the latter is expressed on a uniform logarithmic scale. This defines simple analytic formulae for the typical Matthews coefficient and for the typically allowed number of parameters per atom for crystals diffracting to a given resolution. This simple dependence makes it possible in many cases to estimate the expected resolution of the experimental data for a crystal with a given Matthews coefficient. When expressed using the same logarithmic scale, the most frequent values for R and R(free) factors and for their difference are also essentially linear across a large resolution range. The minimal R-factor values are practically constant at resolutions better than 3 A, below which they begin to grow sharply. This simple dependence on the resolution allows the prediction of expected R-factor values for unknown structures and may be used to guide model refinement and validation.