Abstract
TLS modelling was developed by Schomaker and Trueblood to describe atomic displacement parameters through concerted (rigid-body) harmonic motions of an atomic group [Schomaker & Trueblood (1968), Acta Cryst. B24, 63-76]. The results of a TLS refinement are T, L and S matrices that provide individual anisotropic atomic displacement parameters (ADPs) for all atoms belonging to the group. These ADPs can be calculated analytically using a formula that relates the elements of the TLS matrices to atomic parameters. Alternatively, ADPs can be obtained numerically from the parameters of concerted atomic motions corresponding to the TLS matrices. Both procedures are expected to produce the same ADP values and therefore can be used to assess the results of TLS refinement. Here, the implementation of this approach in PHENIX is described and several illustrations, including the use of all models from the PDB that have been subjected to TLS refinement, are provided.
Highlights
If a motion is harmonic, the probability of a shift of an atom n by a vector rn = Áxn i + Áyn j + Áznk is defined by individual isotropic (Bn) or anisotropic (Un) atomic displacement paramet0ers (ADPs): hÁx2ni hÁxnÁyni hÁxnÁzni Un 1⁄4 @ hÁxnÁyni hÁy2ni hÁynÁzni A: ð1Þ
Depending on the accepted paradigm (x1.3) 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 and (ii) are the particular descriptors of the TLS model consistent with the TLS formalism in addition to (i)
Since modern atomic model refinement packages use an indirect TLS parameterization (x1.3), 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
Summary
Describing atomic positions in crystal structures by Cartesian coordinates is a mathematical abstraction. If a motion is harmonic (in particular, this means that the motion amplitude is small), the probability of a shift of an atom n by a vector rn = Áxn i + Áyn j + Áznk is defined by individual isotropic (Bn) or anisotropic (Un) atomic displacement paramet0ers (ADPs): hÁx2ni hÁxnÁyni hÁxnÁzni Un 1⁄4 @ hÁxnÁyni hÁy2ni hÁynÁzni A: ð1Þ hÁxnÁzni hÁynÁzni hÁz2ni. These characteristics of atomic mobility are part of the structural information that is associated with models of crystal structures. Modern refinement programs treat these motions using three separate components: motion of the whole crystal (modelled as an overall anisotropic scale factor), motion of non-overlapping groups that are considered to be rigid, and individual atomic motions
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