Return to my Home Page.

Contents

• Program References
• Other Useful References
• Hints for running REFMAC
• My TLS refinement is unstable. What do I do?
• Why do I get different results with Refmac5.x?
• Was my TLS refinement OK?
• Was my choice of TLS groups OK?
• Analysing the results with TLSANL
• Interconverting between B_resi, B_TLS and B_total
• What does it all mean?
• How do I make pretty pictures?
• What are these axes?
• Displaying thermal ellipsoids
• Depositing TLS parameters
• Which B factors do I use in Escet?
• Background theory
• Examples
• Example applications

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"

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, 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

• You can use TLS at (almost) any resolution! At very low resolution, you can include a single TLS group (just 20 extra refinement parameters), while at high resolution you can create more detailed TLS models. In fact, it seems that TLS fares worse at high resolution, perhaps because non-rigid-body displacements are more significant at high resolutions.
• When you do start TLS refinement, we find it best to set individual B factors to a constant value, with

  BFAC SET 40

  and refine them after refining the TLS parameters. If only minor re-building is done after the first round of TLS refinement, then TLS and B parameters can be kept for input to subsequent refinement cycles.

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 re-building, 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?

• 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 problem-dependent.
• 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 non-positive 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?

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

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

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 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
bresid
end
EOF

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          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.

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

• tlsanl-r1.31.f
• tlsanl-r1.10.inc

What does it all mean?

• 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 anti-phase 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.

How do I make pretty pictures?

What are these axes?

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

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/dem-web/toc.html

Xfit:

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

povscript:

http://people.brandeis.edu/~fenn/povscript

Depositing TLS parameters

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?

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

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 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 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 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.

Examples

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

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