From deep TLS validation to ensembles of atomic models built from elemental motions

Acta Crystallogr D Biol Crystallogr. 2015 Aug;71(Pt 8):1668-83. doi: 10.1107/S1399004715011426. Epub 2015 Jul 28.


The translation-libration-screw model first introduced by Cruickshank, Schomaker and Trueblood describes the concerted motions of atomic groups. Using TLS models can improve the agreement between calculated and experimental diffraction data. Because the T, L and S matrices describe a combination of atomic vibrations and librations, TLS models can also potentially shed light on molecular mechanisms involving correlated motions. However, this use of TLS models in mechanistic studies is hampered by the difficulties in translating the results of refinement into molecular movement or a structural ensemble. To convert the matrices into a constituent molecular movement, the matrix elements must satisfy several conditions. Refining the T, L and S matrix elements as independent parameters without taking these conditions into account may result in matrices that do not represent concerted molecular movements. Here, a mathematical framework and the computational tools to analyze TLS matrices, resulting in either explicit decomposition into descriptions of the underlying motions or a report of broken conditions, are described. The description of valid underlying motions can then be output as a structural ensemble. All methods are implemented as part of the PHENIX project.

Keywords: TLS matrices; TLS model; correlated motion; diffuse scattering; ensemble of models; libration; model validation; molecular mobility; vibration.

Publication types

  • Research Support, N.I.H., Extramural
  • Research Support, Non-U.S. Gov't
  • Research Support, U.S. Gov't, Non-P.H.S.

MeSH terms

  • Algorithms
  • Animals
  • Calmodulin / chemistry
  • Humans
  • Models, Molecular
  • Motion
  • Prokaryotic Initiation Factor-2 / chemistry
  • Protein Conformation
  • Proteins / chemistry*


  • Calmodulin
  • Prokaryotic Initiation Factor-2
  • Proteins