
REFMAC (CCP4: Supported Program)
User's manual for the program refmac_5.0.36
What does TLS refinement mean?
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 makeup 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.
TLS refinement in REFMAC
REFMAC needs the following information to do TLS refinement:
 REFI TLSC 20
 The TLSC subkeyword initiates cycles of TLS refinement, in this
example 20 cycles. These cycles are performed after initial estimation
of scaling parameters and before refining coordinates and B factors.
 TLSIN
 The TLSIN file specifies the rigid groups to be used.
The full specification of this file is given in the
Files section. Generally, you only need
to give the TLS record (which starts a group definition) and the
RANGE record which specifies which atoms are included in the group.
 BFAC SET 40
 We have found that TLS refinement works best if individual B factors
are first set to a constant value. This is done with the BFAC keyword.
B factors are then refined after the TLS parameters have been determined.
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.
Output from REFMAC
Refinement statistics are as in a traditional refinement run. In addition,
you get:
 Refined TLS parameters written to the TLSOUT file. This file can
be analysed with the auxiliary program TLSANL, see below.
 B factors in the XYZOUT file. These are "residual" B factors that
are refined after determining the TLS parameters, and do not contain
any contribution from the TLS parameters.
N.B. When attempting to interpret the TLS tensors physically, it
is important to bear in mind the following:
 TLS parameters are refined assuming the physical model of a rigid
body, i.e. that all atoms in the TLS groups have amplitudes (in 3 dimensions)
appropriate to a rigid body and that all atoms move in phase.
However, if for example one constructed a model in which all atoms in
the TLS group had rigid body amplitudes but with one half moving in
antiphase with the other half, one would get the same derived U values
and hence the same fit to the observed structure factors. The same is true
of more complicated phase relationships between the atomic displacements.
Thus the refinement statistics would be just as good, but the physical
interpretation may be quite different.
 TLS parameters, like any other form of displacement parameter, will
mop up errors as well as a variety of different displacement types. This
is particularly true when TLS is the only modelling of anisotropy that
is being used  the TLS parameters will attempt to fit anisotropic
internal modes and anisotropic errors.
Analysing the results with TLSANL
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:
 1. INPUT TENSOR MATRICES WRT ORTHOGONAL AXES USING ORIGIN OF CALCULATIONS
 This should echo the contents of the tls file, with the values
now displayed as matrices.
 2. FOR TLS TENSOR USING CENTRE OF REACTION:
 (About halfway down.) T and L are real symmetric tensors, and so
can be diagonalised to give principal axes. S is also symmetric for
one particular choice of origin (the Centre of Reaction), and can then
also be diagonalised. This section gives the orientation of the principal
axes of T, L and S in various coordinate frames, and also the magnitudes
along these axes. So for example, if the input TLS tensors are:
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 MEANSQUARE 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.
How do I make pretty pictures?
Latest version of TLSANL has keyword AXES for outputting
the various axes in a format suitable for molscript.
References
 [1]
 Winn, M.D., Isupov, M.N. and Murshudov G.N. (2001) Acta Cryst.,
D57, ????.
 [2]
 Howlin, B., Moss, D.S. and Harris, G.W. (1989) Acta Cryst.,
A45, 851  861.
 [3]
 Schomaker, V. and Trueblood, K.N. (1968) Acta Cryst.,
B24, 63  76.
 [4]
 Schomaker, V. and Trueblood, K.N. (1998) Acta Cryst.,
B54, 507  514.
 [5]
 B.Howlin, S.A.Butler, D.S.Moss, G.W.Harris and H.P.C.Driessen (1993)
J. Appl. Cryst., 26, 622
