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Updated: Apr 23, 2026

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Published on: December 6, 2024
TLS from fundamentals to practice
Alexandre Urzhumtsev1, Pavel V Afonine2, Paul D Adams3
1IGBMC, CNRS-INSERM-UdS, 1 rue Laurent Fries, B.P.10142, 67404 Illkirch, France ; Université de Lorraine, B.P. 239, Faculté des Sciences et des Technologies, 54506 Vandoeuvre-lès-Nancy, France.
Abstract:
The Translation-Libration-Screw-rotation (TLS) model of rigid-body harmonic displacements introduced in crystallography by Schomaker & Trueblood (1968) is now a routine tool in macromolecular studies and is a feature of most modern crystallographic structure refinement packages. In this review we consider a number of simple examples that illustrate important features of the TLS model. Based on these examples simplified formulae are given for several special cases that may occur in structure modeling and refinement. The derivation of general TLS formulae from basic principles is also provided. This manuscript describes the principles of TLS modeling, as well as some select algorithmic details for practical application. An extensive list of applications references as examples of TLS in macromolecular crystallography refinement is provided.
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