Use of TLS parameters to model anisotropic displacements in macromolecular refinement

An essential step in macromolecular refinement is the selection of model parameters which give as good a description of the experimental data as possible while retaining a realistic data-to-parameter ratio. This is particularly true of the choice of atomic displacement parameters, where the move from individual isotropic to individual anisotropic refinement involves a sixfold increase in the number of required displacement parameters. The number of refinement parameters can be reduced by using collective variables rather than independent atomic variables and one of the simplest examples of this is the TLS parameterization for describing the translation, libration and screw-rotation displacements of a pseudo-rigid body. This article describes the implementation of the TLS parameterization in the macromolecular refinement program REFMAC. Derivatives of the residual with respect to the TLS parameters are expanded in terms of the derivatives with respect to individual anisotropic U values, which in turn are calculated using a fast Fourier transform technique. TLS refinement is therefore fast and can be used routinely. Examples of TLS refinement are given for glyceraldehyde-3-phosphate dehydrogenase (GAPDH) and a transcription activator GerE, for both of which there is data to only 2.0 Å, so that individual anisotropic refinement is not feasible. GAPDH has been refined with between one and four TLS groups in the asymmetric unit and GerE with six TLS groups. In both cases, inclusion of TLS parameters gives improved refinement statistics and in particular an improvement in R and free R values of several percent. Furthermore, GAPDH and GerE have two and six molecules in the asymmetric unit, respectively, and in each case the displacement parameters differ significantly between molecules. These differences are well accounted for by the TLS parameterization, leaving residual local displacements which are very similar between molecules and to which NCS restraints can be applied.