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See main citation below.
Contents
Program References
 TLS in Refmac
 M.D.Winn, M.N.Isupov and G.N.Murshudov,
Acta Cryst. D57, 122  133 (2001).
 "Use of TLS parameters to model anisotropic displacements in
macromolecular refinement"
reprint in PDF format
Copyright © International Union of Crystallography
 TLS in Refmac (2)
 M.D.Winn, G.N.Murshudov and M.Z.Papiz, Methods in Enzymology
374 300321 (2003)
 "Macromolecular TLS refinement in REFMAC at moderate resolutions"
 TLSANL
 B.Howlin, S.A.Butler, D.S.Moss, G.W.Harris and H.P.C.Driessen (1993)
J.Appl.Cryst., 26, 622
Other Useful References
 Shows the value of TLS refinement
 R.P.Joosten et al. (2009)
J.Appl.Cryst., 42, 376384
 "PDB_REDO: automated rerefinement of Xray structure models in the PDB"
 Compares the predictions of TLSMD for choice of TLS
groups (and other methods) to a database of known hinge locations
 S.C.Flores et al., (2008)
Proteins  structure, function and bioinformatics, 73 299319
 Discusses to what extent a TLS model can be
interpreted biochemically
 P.B.Moore, (2009)
Structure, 17 13071315
Hints for running REFMAC
My TLS refinement is unstable. What do I do?
 First, read the logfile very carefully, and check for
obvious syntactical errors in the input!
 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.
 There have been cases where TLS refinement has been stabilised
by switching from bulk scaling to simple scaling for the first
round of refinement.
 We have occasionally observed instabilities in the TLS refinement
when the model is apparently complete and everything else looks OK.
The best advice in this case is to run TLS refinement for just
a few cycles. Then do restrained refinement and some rebuilding,
and then try another round of TLS refinement. It is
possible in some cases to bootstrap it up.
 There are also reported problems with small TLS groups.
Why do I get different results with Refmac5.x?
 I get small/negative T values in Refmac5.2 / My atomic B factors are
larger in Refmac5.2
 The overall B factor has contributions from overall B, TLS parameters
and atomic residual B factors, and there is some ambiguity in how it is
partitioned between these contributions. In particular, the isotropic
component of the T tensor can be reduced, with a concommitant increase
in atomic B factors, without changing the overall model.
This is what has been done for Refmac 5.2 If you compare the results
with earlier versions of Refmac, you will find you have lower diagonal
T values and higher atomic B values.
Although this is potentially confusing, this is not anything to worry
about.
Was my TLS refinement OK?
Things to check after refinement:
 Did your free R factor fall? Note that the final plot of R factors
against cycle should show clearly 2 parts, corresponding to the TLS
refinement and restrained refinement stages.
 Has your electron density improved? Note that if the TLS simply
models the smearing of your electron density, then the R factors will
improve while the density remains the same. However, if this modelling
improves the determination of the average coordinates, and thus
corrects model errors, then the maps can improve. Obviously, this is
problemdependent.
 Run TLSANL (see below) with the ANISO option, and check that
all the derived Us are sensible. If Us for some atoms are not, e.g. they
are flagged nonpositive definite, then they should be removed from
the TLS group.
 Note that the average B factor of the output PDB file from REFMAC
will appear to be unusually low, and in particular lower than the
Wilson B. This is because this B factor, the "residual" B factor, does
not include the contribution to atomic displacements from TLS. Run the
files from REFMAC through the program
TLSANL
and the resulting PDB file will contain the total B factor including
the equivalent isotropic contribution from TLS. (TLSANL can be run from
the interface as the task "Analyse TLS parameters".) But remember
that these B factors are derived information, and not refinement
parameters!
Was my choice of TLS groups OK?
There is probably not a single "correct" choice of TLS groups. TLS models
certain aspects of atomic displacements, and different choices of TLS
groups may model different, but equally valid, aspects of the displacements.
One should be able to reject poor choices of groups, e.g. where many
atoms have unphysical derived Us. One can then try to optimise the choice
of TLS groups based on the free R factor and electron density map quality.
The general approach would be to start with one TLS group per molecule,
and then look to break up each molecule into welldefined subunits (usually
domains).
(I intend to work on tools for aiding the choice of TLS groups soon.)
Analysing the results with TLSANL
These notes refer to the latest version of
TLSANL
which has changed considerably since CCP4 version 4.0
At the end of refinement, you should have a file (assigned to TLSOUT)
containing information for each TLS group something like:
REFMAC
TLS All protein
RANGE 'A 1.' 'A 118.'
ORIGIN 18.885 49.302 13.315
T 0.0263 0.0561 0.0048 0.0128 0.0065 0.0157
L 0.9730 5.1496 0.8488 0.2151 0.1296 0.0815
S 0.0007 0.0281 0.0336 0.0446 0.2288 0.0551 0.0487 0.0163
The various records are:
 REFMAC
 This alerts the program TLSANL (see below) to the fact that the
file came from REFMAC. Older versions of refmac5 wrote the line
"! Output from REFMAC". If you get this, edit it to "REFMAC".
Otherwise you will get garbage.
 TLS
 Start of TLS group, and useful title.
 ORIGIN
 Origin of TLS group calculated by program. This is referred to
as "ORIGIN OF CALCULATIONS" in the TLSANL output.
 T and L
 Values of the T and L tensors. These are symmetric, and the
numbers are the 11, 22, 33, 12, 13, 23 elements respectively.
 S
 Values of the S tensor. This is an asymmetric tensor, and the
numbers are the 2211, 1133, 12, 13, 23, 21, 31, 32 elements
respectively. Note that the elements 11, 22, 33 cannot be fixed
by Bragg peak intensities only, and only the differences 2211, 1133
and hence 2233 are known. Usually 11, 22 and 33 are quoted by
setting the trace 11+22+33 arbitrarily to zero.
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.
For each group, this gives several representations of the T, L and S
tensors. Full details are can be
found in Howlin et al. 1993, so here I'll
try to pick out the important bits. Things 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, we may have the input TLS tensors:
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.
Interconverting between B_resi, B_TLS and B_total
The file XYZOUT from REFMAC5 contains residual Bs ("B_resi")
in the B factor column. The file XYZOUT from TLSANL can
include either B_resi, B_TLS (B factors derived from the TLS parameters) or
B_total=B_TLS+B_resi depending on the keyword ISOOUT. This file also includes individual
anisotropic U factors (in PDB format ANISOU cards) with contents also determined
by the ISOOUT keyword. By default, TLSOUT generates a PDB file with the total
anisotropic U factors and B factors.
It is useful to generate total B and U factors, in order to use older programs
which don't understand TLS. However, it is necessary to have B_resi in order to
run another round of TLS refinement. To recover B_resi from a file containing B_total,
you can run a script (but see below):
tlsanl xyzin foo_tlsanl.pdb tlsin foo_refmac.tls xyzout foo_resi.pdb <<EOF
bresid false
isoout resi
END
EOF
However, this option is unfortunately broken in CCP4 6.0.2 Patched source code files
are available at:
What does it all mean?
Part of TLS refinement is improving refinement behaviour by accounting
for anisotropy in the data and, in the case of NCS, accounting for
overall differences in displacements between molecules. However, it
is also tempting to try 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.
So what's the bottom line? Beware of overinterpreting your results!
Use TLS as supporting evidence maybe, but don't base your reaction
mechanism on it!
How do I make pretty pictures?
Latest version of TLSANL has keyword AXES for outputting
the various axes in a format suitable for molscript.
What are these axes?
I have another question for you regarding the TLS tensors. The libration axes
outputted for molscript by TLSANL have their origin at the center of reaction
(choosen such that the S tensor is symmetric). This means some of the axes are
shifted from the center of mass which is what Refmac uses in the refinement
(if I understand the documentation correctly). For visualization purposes is
it valid to just translate the axes to the center of mass used by REFMAC? The
TLSANL documentation states that "The L tensor is in general independent of
the origin, and in particular is the same for both origins considered here". I
don't quite see how the axes can be independent of the origin, are there any
papers that would explain this in more detail?
Best to refer to the original Schomaker and Trueblood paper
Acta Cryst B24 63 (1968) see p67 especially.
The basic idea is as follows: imagine rotating 90 degrees
about some axis. If you now rotate 90 degrees about a parallel
axis, you get the same change in orientation, but with an
additional translation. If you now invert that, and say you
are trying to describe a particular change in orientation, then
you need a certain rotation but you can choose any parallel
axis.
Now L describes a mean square libration rather than a single
rotation, but it is similar. To model the orientational
component of the group dispacements, you have an L, and it
doesn't matter which axes it is about. However, if you choose
different axes, then you introduce additional translations,
which then affect T (mean squared translation) and S (covariance
between translation and libration).
The danger is to view the axes as simple rotation axes. They
are the principal axes of the L tensor, and are intimately
connected with the T and S. There is not really a unique physically
correct choice of axes. The choice of the Centre of Reaction is
simply so that S is symmetric and can be diagonalised to give
principal axes to display.
To answer your question, you could shift the L axes to the
centre of mass, but that is not any more correct. You could
shift the T axes, but you would have to change their values
(T gets larger). You can't shift the S axes because S is no
longer realsymmetric.
In any case, for large groups there is usually little difference
between the centre of mass and the centre of reaction. Only for
small groups of a few atoms (e.g. side chain groups) does it
get interesting...
Displaying thermal ellipsoids
The output PDB file from the program TLSANL contains anisotropic U parameters
in ANISOU records. These are derived from the TLS parameters, and are
NOT independent! They can be displayed graphically as thermal
ellipsoids. There are a number of programs that will do this:
 Rastep in RASTER3D:

http://www.bmsc.washington.edu/raster3d/raster3d.html
grep NAD file.pdb  rastep auto Bcol 5. 35. > ellipsoids.r3d
render jpeg < ellipsoids.r3d > ellipsoids.jpeg
 ORTEP:

http://www.ornl.gov/ortep/ortep.html
 Mapview:

http://www.chem.gla.ac.uk/~paule/chart/
 xtalview:

http://www.scripps.edu/pub/demweb/toc.html
 Xfit:

http://www.ansto.gov.au/natfac/asrp7_xfit.html
 povscript:

http://people.brandeis.edu/~fenn/povscript
Depositing TLS parameters
The file XYZOUT from Refmac contains the refined
TLS parameters in the PDB header (as REMARK 3 records).
These should be accepted by the deposition centre.
Refmac also writes out a Data Harvesting file which contains the TLS parameters in mmCIF
format, and will also be accepted by the deposition centre.
Note that the definitions for TLS parameters are included in the
CCP4 Harvest Dictionary as categories CCP4_REFINE_TLS
and CCP4_REFINE_TLS_GROUP, and in the
PDB mmCIF Extension Dictionary as categories PDBX_REFINE_TLS
and PDBX_REFINE_TLS_GROUP.
Which B factors do I use in Escet?
ESCET is a program for finding the rigid part of
protein molecules by constructing difference distance matrices from related
structures. It uses atomic B factors as part of its errorscaling.
I have been asked whether full or residual B factors should be used in
ESCET. You could argue that the TLSderived B factors describe rigid
body motions of the monomers (for the case of one TLS group per
monomer), and therefore do not contribute to the uncertainty in
intramonomer distances. However, in practice, the TLS parameters
include various contributions, beyond the ideal rigidbody motion, so
I would say you should include them. I.e. give ESCET the B factors
from TLSANL.
However, it might just be a pragmatic decision as to which
gives you a cleaner answer. In this case, the questioner found that
ESCET gave similar (though not identical) results when comparing full
and residual B factorbased calculations. The plots were slightly cleaner
with the residual B factors.
(Thanks to Qingrong Fan.)
Background theory
The theory behind the TLS parameterisation has been presented in
detail by Schomaker and Trueblood (Schomaker and Trueblood, 1968),
with useful summaries in Howlin et al. (1989) and Schomaker and
Trueblood (1998).
Any displacement of a rigid body can be described as a rotation about
an axis passing through a fixed point, together with a translation
of that fixed point. The corresponding displacement of a point at
r relative to the fixed point is given by
where t is a column vector for the translation and D is the
rotation matrix. For small displacements, the last term in (1) can
be linearised with respect to the amplitude of the rotation to give
where lambda is a vector along the rotation axis with a magnitude
equal to the angle of rotation, and X denotes a cross product.
The corresponding dyad product is then
where superscript T denotes the row vector. Finally, performing a time
and spatial average over all displacements yields
where ,
and
. In this context, the cross product is used as follows:
yields a matrix whose i'th row is the cross product of the i'th row
of L and r.
Equation (4) gives the mean square displacement of a point r in a
rigid body in terms of three tensors T, L and S.
Considering in particular the set of points {r} corresponding to the
rest positions of atoms in a single rigid body, U is the mean square displacement
of each such atom, and can be identified as the anisotropic
displacement parameter that occurs in the DebyeWaller factor in the
expression for the structure factor. The linearisation used to obtain
equation (2) is equivalent to retaining only quadratic
terms in the expression for the ADP.
Given a set of refined ADPs, equation (4) can be used to
make a least square fit of TLS parameters. Alternatively, and the
approach we use here, equation (4) can be used to derive
ADPs and hence calculated structure factors from TLS refinement
parameters. T and L are symmetric tensors, while
S is in general asymmetric. Expanding equation (4)
out fully shows that the trace of S is not fixed by U.
Hence, there are a total of 20 refinable parameters (6 from T,
6 from L and 8 from S).
Thus, the first derivative is obtained from
where is the i'th parameter ( ) of the
m'th TLS group, and is the (jk) element of the anisotropic
displacement parameter of atom n. In equation (5), the sum runs
over all atoms in the m'th TLS group. The first factor on the righthand
side of equation (6) is obtained as described previously, while the second
factor is obtained easily from equation (4).
Similarly, the second derivatives are
The summation is restricted to terms with both U factors associated with
the same atom, and consequently only second derivatives for the same
TLS group are collected. This restriction could, of course, be lifted
easily.
Equation (1) expanded to quadratic terms in lambda
and averaged gives an expression for the mean position of each
atom (Howlin et al., 1989):
The correction relative to the rest position r is O(L)
and can therefore be neglected in the expression (4)
for U, i.e. no distinction is made between rest and mean
positions. However, this distinction needs to be taken into account
when applying distance restraints, which apply to distances between
rest positions r rather than between the observed mean positions
x (the former being a better measure of the mean distance).
Given the observed distance d0, the distance been rest
positions d can be estimated as (Howlin et al., 1989):
where n is a unit vector along the bond in question. For
small TLS groups such as amino acid side chains, d can be greater
than d0 by 0.01 Å or more (Howlin et al., 1989), and therefore can
have a significant effect on the agreement between ideal and observed
distances. For larger TLS groups, such as we consider later, values of
L and hence the distance correction tend to be an order of
magnitude smaller, and the correction is probably less important.
Examples
Nonintersecting screw axes derived from TLS tensors for GAPDH:
Contents of asymmetric unit (2 molecules) have been modelled as
one TLS group. Free R factor is reduced by 4.5% compared to a
refinement with isotropic B factors only.
Example applications
 bovine ribonuclease A at 1.45A with side chain groups
 Howlin, B., Moss, D.S. and Harris, G.W. (1989) Acta.Cryst.,
A45, 851  861.
 endothiopepsin at 1.8A
 Sali, A., Veerapandian, B., Cooper, J.B., Moss, D.S.,
Hofmann, T., and Blundell, T.L. (1992) Proteins: Structure, Function and
Genetics, 12, 158
 crambin
 Stec, B., Zhou, R., and Teeter, M.M. (1995) Acta Cryst.,
D51, 663
 calmodulin  2nd reference has comparison of 3 TLS models
 Wilson, M.A. and Brunger, A.T. (2000) J.Mol.Biol.,
301, 1237
Wilson, M.A. and Brunger, A.T. (2003) Acta.Cryst.,
D59, 1782
 mannitol dehydrogenase  example of NCS differences
 Horer, S., Stoop, J., Mooibroek, H., Baumann, U. and Sassoon, J.
(2001) J. Biol. Chem. 276, 27555
 S100A12 at 1.95A
 Moroz, O.V., Antson, A.A., Murshudov, G.N., Maitland, N.J.,
Dodson, G.G., Wilson, K.S., Skibshoj, I., Lukanidin, E.M., and Bronstein, I.B.
(2001) Acta Cryst. D57, 20
 proteinDNA complex at 1.85A
 Schwartz, T., Behlke, J., Lowenhaupt, K., Heinemann, U.
and Rich, A. (2001) Nature Structural Biology 8 761
 thioredoxin reductase at 3.0A (1h6v)
 Sandalova, T., Zhong, L., Lindqvist, Y.,
Holmgren, A. and Schneider, G. (2001) Proc. Nat. Acad. Sci.
98 9533
 Lightharvesting complex
 M.Z.Papiz et al, J.Mol.Biol., 326, 1523 (2003)
 GroEL / GroES
 C.Chaudhry et al. J.Mol.Biol., 342, 229 (2004)
 Thioredoxin reductase at 3.0A
 Akif M, Suhre K, Verma C and Mande S C,
(2005) Acta Cryst. D61, 1603
martyn.winn@stfc.ac.uk
Last modified: Tue May 12 15:04:39 BST 2009