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

Abstract

The widely used Translation Libration Screw (TLS) approximation describes concerted motions of atomic groups in X-ray refinement. TLS refinement often provides a better interpretation of diffraction data and the resulting rigid body motions may subsequently be assigned biochemical significance. In TLS refinement, three matrices (T, L and S) describe harmonic vibration, libration and their correlation. Because these matrices describe specific motions, they impose a number of conditions on their elements. Ignoring these conditions while refining the matrix elements may result in matrices that cannot be interpreted in terms of physically realistic motions. We describe a mathematical framework and the computational tools to analyze refined TLS matrices through their decomposition into descriptors of underlying motions. This allows for straightforward validation and identification of implausible TLS parameters. An algorithm for the generation of structural ensembles that are consistent with given TLS parameters, implemented as a part of the Phenix project, is also described.\n\nSynopsisProcedures for the decomposition of TLS matrices into elementary vibrations and librations indicates possible errors in the definition of these matrices and corrects them when possible. The program outputs the corresponding vibration-libration parameters and generates structural ensembles.