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title: TLS background | ||
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Displacement of groups of atoms can be modeled by the TLS formalism presented | ||
in detail by Schomaker and Trueblood (1968). The TLS formalism describes a | ||
rigid-body displacement with three tensors T, L, and S for Translation, | ||
Libration, Screw. Useful qualitative and quantitative explanations of the TLS | ||
formalism summaries are presented by Winn, Isupov and Murshudov (2001), | ||
Painter and Merritt (2005, 2006). All of the papers above are references for | ||
this page. | ||
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T and L are symmetric 3x3 tensors with units in Å^2^ and radians^2^, | ||
respectively. The | ||
translation tensor T describes the anisotropic translational displacement for | ||
the atoms in the rigid body and is analogous to the individual anisotropic | ||
mean-square displacement tensor [U][1]. The rotation of the rigid body is | ||
described by the libration tensor L. The screw tensor S describes the | ||
correlation between the rotation and translation of a rigid body undergoing | ||
rotation about three non-intersecting orthogonal axes. | ||
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Here, we consider the total [ADP][1] to have 3 contributions: | ||
U = U~crystal~ + U~TLS~ + U~atom,residual~ | ||
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The overall anisotropy U~crystal~ is generally modeled using a single | ||
anisotropic scale factor. The isotropic component of the overall scale factor | ||
is usually included in the B-factors, but in [some][2] PDB files this is not | ||
the case. U~TLS~ can be related to the T, L, and S tensors, their origin, | ||
and an atom in the TLS group located at x, y, z as: | ||
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U~TLS~^11^ = L^22^z^2^+ L^33^y^2^- 2L^23^yz+ 2S^21^z- 2S^31^y+ T^11^ | ||
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U~TLS~^22^ = L^11^z^2^+ L^33^x^2^- 2L^31^xz- 2S^12^z+ 2S^32^x+ T^22^ | ||
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U~TLS~^33^ = L^11^y^2^+ L^22^x^2^- 2L^12^xy- 2S^23^x+ 2S^13^y+ T^33^ | ||
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U~TLS~^12^ = -L^33^xy+ L^23^yxz- L^13^yz- L^12^z^2^- S^11^z+ S^22^z+ S^31^x- S^32^y+ T^12^ | ||
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U~TLS~^13^ = -L^22^xz+ L^23^yx- L^13^y^2^+ L^12^yz+ S^11^y- S^33^y+ S^23^z- S^21^x+ T^13^ | ||
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U~TLS~^23^ = -L^11^yz- L^23^x^2^+ L^13^xy+ L^12^xz- S^22^x+ S^33^x+ S^12^y- S^13^z+ T^23^ | ||
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A TLS model can be interpreted as a sum of 6 independent displacements: | ||
3 screw librations about non-intersecting axes and 3 translations. The program | ||
[TLSView][3] (Painter and Merrit, 2005) is very useful for visualizing the TLS | ||
motion. | ||
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Modeling U~atom,residual~ is described [here][1]. The B-factor in PDB files is | ||
usually the sum of the isotropic components of U~crystal~, U~TLS~, and | ||
U~atom,residual~. | ||
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### Additional analyses: PDB versus BDB | ||
Several analyses of the (differences between) PDB and BDB files are described | ||
in the [BDB paper][4]. | ||
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In the article we show that the global B-factor maximum smoothed in a | ||
5-residue window in a PDB chain is often tens of residues away from the | ||
maximum in the corresponding BDB chain. | ||
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This figure shows correlation of the Cα-Cα distance between the | ||
maxima with the distance in primary structure. | ||
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![][5] | ||
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### References and Further Reading | ||
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* Painter, J. and Merritt, E.A. (2005) Acta Crystallogr. D, 61, 465-471. | ||
* Painter, J. and Merritt, E.A. (2006) Acta Crystallogr. D, 62, 439-450. | ||
* Schomaker, V. and Trueblood, K.N. (1968) Acta Crystallogr. B, 24, 63-76. | ||
* Winn, M.D., Isupov, M.N. and Murshudov, G.N. (2001) Acta Crystallogr. D, 57, 122-133. | ||
* Zucker, F., Champ, P. and Merritt, E.A. (2010) Acta Crystallogr. D, 66, 889-900. | ||
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[1]: {{ url_for("pages", name="theory") }} "U" | ||
[2]: http://phenix-online.org/pipermail/phenixbb/2012-August/018927.html | ||
"overall anisotropic scale" | ||
[3]: http://pymmlib.sourceforge.net/doc/tlsview/tlsview.html "TLSView" | ||
[4]: {{ url_for("pages", name="about") }} "About BDB" | ||
[5]: {{ url_for("static", filename="background/penta_caca_seq_dist.png") }} | ||
"maxima" |
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