Date Published: July 01, 2018
Publisher: International Union of Crystallography
Author(s): Pavel V. Afonine, Paul D. Adams, Alexandre Urzhumtsev.
The values of anisotropic atomic displacement parameters (ADPs) that correspond to concerted motions can be obtained from refined TLS matrices analytically or numerically. The difference between the ADPs obtained using these two methods can be used to assess the results of TLS refinement.
Validation of atomic models is now routine in macromolecular crystallography and is an integral part of structure submission to the Protein Data Bank (Read et al., 2011 ▸; Gore et al., 2017 ▸). It requires nomenclature compliance and fit to experimental data. Atomic coordinates are subjected to validation that includes analysis of stereochemistry and molecular packing. Atomic displacement parameters (ADPs) are also subjected to validation. For isotropic ADPs the existing validation criteria are rather simple: their values must be positive, not excessively large and not vary too much between neighbouring atoms. For anisotropic ADP values the criteria are somewhat more complex (Hirshfeld, 1976 ▸; Schneider, 1996 ▸). Similarly to atomic coordinates and displacement parameters, TLS matrices are model parameters and therefore should be subjected to some form of validation. Depending on the accepted paradigm (§1.3) the scope of TLS validation may refer to two questions: (i) how well does the the TLS approximation explain the experimental data and how well does it describe the atomic displacement parameters (see, for example, Merritt, 2011 ▸, 2012 ▸) and (ii) are the particular descriptors of the TLS model also consistent with the TLS formalism in addition to (i). Addressing the first question does not require analysis of the TLS matrices themselves but only of the derived ADP values. This includes making sure that the ADPs are positive definite and vary smoothly between adjacent atoms and TLS groups (Winn et al., 2001 ▸; Zucker et al., 2010 ▸; Merritt, 2011 ▸, 2012 ▸). The current work addresses the second question, which focuses exclusively on the analysis of TLS matrices and the parameters of group motion that they encode. Since modern atomic model refinement packages use an indirect TLS parameterization (§1.3), i.e. they refine the elements of the TLS matrices and not the parameters of group motions, it is unsurprising to find that some TLS matrices do not comply with the assumption of harmonic motion that the TLS modelling theory is built upon. The number of such cases may vary based upon the different measures or thresholds that are used. For example, using the criteria discussed above we find that only 2.3% of the TLS groups reported in the PDB can be interpreted in terms of elemental harmonic motions. We envisage two reasons for this. Firstly, the validation of TLS refinement results, focusing on TLS matrices and corresponding group motions, has never been enforced. Secondly, the implementation of TLS refinement in modern refinement packages does not allow control of the parameters of group motion by means of restraints or constraints (see a discussion in Painter & Merritt, 2006 ▸) because these parameters are refined indirectly. Unsurprisingly, such unrestrained refinement provides no guarantee of TLS matrices that are interpretable in terms of harmonic elemental motions.