The theory behind the TLS parameterisation has been presented in detail by Schomaker and Trueblood (Schomaker and Trueblood, 1968) [3], with useful summaries in Howlin et al. (1989) [2] and Schomaker and Trueblood (1998) [4].
TLS parameters describe the possible mean square displacements of rigid bodies. In this context, the rigid bodies are groups of atoms in your protein model. How many groups and the make-up of each group must be chosen by the user. TLS parameters describe anisotropic motion - an anisotropic U factor can be derived for each atom in a TLS group. But these U factors are correlated by virtue of belonging to the same rigid body, and only 20 refinement parameters are required for each TLS group. Thus, refinement of TLS parameters is a method of including anisotropic displacements without requiring the large number of parameters of full anisotropic refinement.
TLS refinement can therefore be used at moderate resolution, e.g. 2.0Å. The number of extra parameters depends on the number of TLS groups defined. A single TLS group for the whole molecule may prove useful, and only requires 20 extra parameters. Or you may define a TLS group for every rigid side chain, using a few thousand extra parameters. TLS refinement may or may not turn out to be useful, but it is unlikely to do any harm. Individual B factors are refined in addition to the TLS parameters.
TLS refinement is often useful when there is NCS. It is often the case that different copies of a molecule in the asymmetric unit have different overall displacements. These can be accounted for by refining TLS parameters for each molecule. The residual atomic displacement parameters (B factors) should then be similar between molecules, and NCS restraints can be applied between them.
REFMAC needs the following information to do TLS refinement:
N.B. There have been some cases where TLS refinement has been tried in the early stages of refinement, and has not been very stable. If this happens, then leave it out, and try again later on when the model is more complete.
Refinement statistics are as in a traditional refinement run. In addition, you get:
N.B. When attempting to interpret the TLS tensors physically, it is important to bear in mind the following:
The TLS file and PDB file output from REFMAC can be inputted to the auxiliary program TLSANL for analysis, via:
tlsanl tlsin in.tls xyzin in.pdb xyzout out.pdb <<EOF bresid end EOF
The keyword "bresid" is essential when running TLSANL on the output of REFMAC (it signifies the fact that the B factors in xyzin do not contain any contribution from the TLS parameters in tlsin).
For each group, this gives several representations of the T, L and S tensors. It also outputs individual anisotropic U factors derived from the TLS tensors to the file XYZOUT. Full details are can be found in Howlin et al. 1993 [5], but here are the important bits to look for:
INPUT TENSOR MATRICES WRT ORTHOGONAL AXES USING ORIGIN OF CALCULATIONS
T TENSOR L TENSOR S TENSOR
(A^2) (DEG^2) (A DEG)
0.026 -0.013 0.007 0.973 0.215 -0.130 0.009 0.034 -0.045
-0.013 0.056 -0.016 0.215 5.150 0.082 -0.055 0.010 -0.229
0.007 -0.016 0.005 -0.130 0.082 0.849 0.049 0.016 -0.019
The principal axes of the L tensor are then:
AXES OF LIBRATION WRT TO MEAN-SQUARE ANGLE LIBRATION AXES MAKE TO
ORTHOGONAL AXES (IN ROWS) DISPLACEMENT ORTHOGONAL AXES (DEG)
ABOUT AXES (DEG^2) X Y Z
0.834 -0.033 -0.550 1.050 33.47 91.88 123.40
0.051 0.999 0.017 5.162 87.09 3.07 89.01
0.549 -0.042 0.835 0.759 56.69 92.43 33.42
In this example, there is a dominant libration along the b axis, and
we see that the second principal axis is aligned almost exactly along b.
The middle column gives the eigenvalues of L, and these can be quoted
rather than the entire tensor.Latest version of TLSANL has keyword AXES for outputting the various axes in a format suitable for molscript.