Experimental determination of optimal root-mean-square deviations of macromolecular bond lengths and angles from their restrained ideal values

Abstract

A number of inconsistencies are apparent in the recent research paper by Jaskolski et al. [(2007), Acta Cryst. D63, 611-620] concerning their recommendations for the values of the magnitude and resolution-dependence of the root-mean-square deviations (RMSDs) of bond lengths and angles from their restrained ideal values in macromolecular refinement, as well as their suggestions for the use of variable standard uncertainties dependent on atomic displacement parameters (ADPs) and occupancies. Whilst many of the comments and suggestions in the paper regarding updates for the ideal geometry values proposed by Engh and Huber are entirely reasonable and supported by the experimental evidence, the recommendations concerning the optimal values of RMSDs appear to be in conflict with previous experimental and theoretical work in this area [Tickle et al. (1998), Acta Cryst. D54, 243-252] and indeed appear to be based on a misunderstanding of the distinction between RMSD and standard uncertainty (SU). In contrast, it is proposed here that the optimal values of all desired weighting parameters, in particular the weighting parameters for the ADP differences and for the diffraction terms, be estimated by the purely objective procedure of maximizing the experiment-based log(free likelihood). In principle, this allows all weighting parameters that are not known accurately a priori to be scaled globally, relative to those that are known accurately, for an optimal refinement. The RMS Z score (RMSZ) is recommended as a more satisfactory statistic than the RMSD to assess the extent to which the geometry deviates from the ideal values and a theoretical rationale for the results obtained is presented in which the optimal RMSZ is identified as the calculated versus true Z-score correlation coefficient, the latter being a monotonic function of the resolution cutoff of the data. Regarding the proposal to use variable standard uncertainties, it is suggested that any departure from the current practice of using fixed weights for geometric restraints based on experimental values of standard uncertainties be subject to the same experiment-based validation.