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

Alexandre Urzhumtsev,Paul D Adams,Andrew H Van Benschoten,Pavel V Afonine,James S Fraser

doi:10.1107/s1399004715011426

Abstract

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.

Highlights

Our results demonstrate that significant issues are present in current TLS
We address the following points
(i) We describe an algorithm (Fig. 1) that interprets the TLS

Summary

Introduction

It is currently difficult to derive a structural basis for concerted molecular motions from the models emerging from macromolecular crystallography, which describe each atom with a central position r0 and additional displacement parameters. Small-magnitude disorder ( thermal motion) can be captured by the Debye–Waller factor, which reflects the probability of an atom moving from its central position by a certain distance. (see, for example, Grosse-Kunstleve & Adams, 2002 and references therein). O is the orthogonalization matrix for the given crystal, h is the column vector of integer indices (h, k, l), UCart is an atomic displacement parameter (ADP) and the superscript stands for the matrix and vector transpose operation (here and in the following). The matrix UCart varies between atoms and is diagonal (with equal elements) for atoms that are assumed to be moving isotropically

Objectives

Findings

Discussion

Conclusion