title: TLSfrom fundamentals to practice.
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 theTLSmodel. Based on these examples simplified formulae are given for several special cases that may occur in structure modeling and refinement. The derivation of generalTLSformulae from basic principles is also provided. This manuscript describes the principles ofTLSmodeling, 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.
authors.affiliation: IGBMC, 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.
authors.forename: Alexandre
authors.initials: A
authors.lastname: Urzhumtsev
authors.affiliation: Lawrence Berkeley National Laboratory, One Cyclotron Road, BLDG 64R0121, Berkeley, CA 94720 USA.
authors.forename: Pavel V
authors.initials: PV
authors.lastname: Afonine
authors.affiliation: Lawrence Berkeley National Laboratory, One Cyclotron Road, BLDG 64R0121, Berkeley, CA 94720 USA ; Department of Bioengineering, University of California Berkeley, Berkeley, CA 94720 USA.
authors.forename: Paul D
authors.initials: PD
authors.lastname: Adams
keywords: ADP; TLS; atomic displacement parameter; rigid body motion; structure refinement; translation libration screw model