R-FREE AND THE R-FREE RATIO - I - DERIVATION OF EXPECTED VALUES OF CROSS-VALIDATION RESIDUALS USED IN MACROMOLECULAR LEAST-SQUARES REFINEMENT

The last five years have seen a large increase in the use of cross val idation in the refinement of macromolecular structures using X-ray dat a. In this technique a test set of reflections is set aside from the w orking set and the progress of the refinement is monitored by the calc ulation of a free R factor which is based only on the excluded reflect ions. This paper gives estimates for the ratio of the free R factor to the R factor calculated from the working set for both unrestrained an d restrained refinement. It is assumed that both the X-ray and restrai nt observations have been weighted correctly and that there is no corr elation of errors between the test and working sets. It is also shown that the least-squares weights that minimize the variances of the refi ned parameters, also approximately minimize the free R factor. The est imated free R-factor ratios are compared with those reported for struc tures in the Protein Data Bank.