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See main citation below.


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 374 300-321 (2003)
- "Macromolecular TLS refinement in REFMAC at moderate resolutions"
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, 376-384
- "PDB_REDO: automated re-refinement of X-ray 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, 73 299-319
Discusses to what extent a TLS model can be interpreted biochemically
P.B.Moore, (2009) Structure, 17 1307-1315

Hints for running REFMAC

My TLS refinement is unstable. What do I do?

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:

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 well-defined 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:


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:
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.
Start of TLS group, and useful title.
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.
Values of the S tensor. This is an asymmetric tensor, and the numbers are the 22-11, 11-33, 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 22-11, 11-33 and hence 22-33 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

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:

This should echo the contents of the tls file, with the values now displayed as matrices.
(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:

          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:

                                   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

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: So what's the bottom line? Beware of over-interpreting 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 real-symmetric.

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:
grep NAD file.pdb | rastep -auto -Bcol 5. 35. > ellipsoids.r3d 
render -jpeg < ellipsoids.r3d > ellipsoids.jpeg


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 error-scaling.

I have been asked whether full or residual B factors should be used in ESCET. You could argue that the TLS-derived 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 intra-monomer distances. However, in practice, the TLS parameters include various contributions, beyond the ideal rigid-body 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 factor-based 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 tex2html_wrap_inline129 , tex2html_wrap_inline131 and tex2html_wrap_inline133 . In this context, the cross product is used as follows: tex2html_wrap_inline135 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 Debye-Waller 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 tex2html_wrap_inline207 is the i'th parameter ( tex2html_wrap_inline211 ) of the m'th TLS group, and tex2html_wrap_inline215 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 right-hand 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.


Non-intersecting screw axes derived from TLS tensors for GAPDH:

Screw axes deduced from TLS refinement

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
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
protein-DNA 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
Light-harvesting 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
Last modified: Tue May 12 15:04:39 BST 2009