Research Article: From deep TLS validation to ensembles of atomic models built from elemental motions. Addenda and corrigendum

Date Published: September 01, 2016

Publisher: International Union of Crystallography

Author(s): Alexandre Urzhumtsev, Pavel V. Afonine, Andrew H. Van Benschoten, James S. Fraser, Paul D. Adams.


Some key parts of the algorithm for interpretation of TLS matrices in terms of elemental atomic motions and corresponding ensembles of atomic models described in the article by Urzhumtsev et al. [(2015) Acta Cryst. D71, 1668–1683] are clarified and developed, and a reference on a wrong model is corrected.

Partial Text

In the original article (Urzhumtsev et al., 2015 ▸), we used several atomic models in order to test the algorithms and provide examples. Unfortunately, the incorrect PDB code had been reported for one of them. Everywhere in the text (§6.2, Tables 2 and 3), 1rge should be used instead of 1dqv and ribonuclease S should be used instead of synaptotagmin. We apologize for this confusion. The diffraction data set used for test refinement of ribonuclease S was obtained from the CCP4 (Winn et al., 2011 ▸) distribution (

The problem of the origin choice is discussed in detail in the review of Urzhumtsev et al. (2013 ▸) leading us to provide less detail in Urzhumtsev et al. (2015 ▸). As mentioned in §2.2 of Urzhumtsev et al. (2015 ▸), the T and S matrices depend on the point (origin of the TLS group) with respect to which the three libration axes are defined. This is also important for generating the matrices from a set of TLS matrices. Confusion arises from the fact that the TLS origin may be, and in fact usually is, different from the origin of the coordinate system in which the atomic coordinates are provided.

The TLS model is valid for harmonic motions and, as a consequence, for small libration amplitudes only. It allows for calculation of the individual atomic displacement parameters in two different ways. They may be calculated analytically using the formulae (2) and (3) from Urzhumtsev et al. (2015 ▸). Alternatively, the same matrices can be calculated numerically from the coordinates of the set of models generated explicitly using the procedure described in §7 and Appendix A of Urzhumtsev et al. (2015 ▸). We stress that in formulae (59)–(61) the expressions are the coordinates of the libration shifts in the basis [L]; similarly, the values in (48) are the coordinates of the vibration shifts in the basis [V]. These coordinates must be converted into the basis [M] in order to obtain the coordinates of the total shifts , n = 1,…N, to be applied to the atomic coordinates , n = 1, … N. Here k is the number of the generated model.




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