Models of Thermal Motion (mostly) in crystals

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Models of Thermal Motion (mostly) in crystals
(with applications to thymidylate synthase)
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Most protein structures are refined with
isotropic thermal parameters. Isotropic
temperature factors correct for the fact that
atoms in the crystal are not point scatterers but
occupy space in the crystal. Both thermal motion
and disorder contribute to a fall off in
scattering efficiency compared to what would be
expected for an atom at rest. Scattering
efficiency is decreased by the factor
Since B depends only in sin ?/? it produced a
spherical correction As B increases, the
contribution of an atom is smeared out more
ordered atoms have smaller B factors.
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Why are they called thermal parameters?
Scattering of a point atom
Calculated exponential
Scattering of a smeared atom
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Electron density around the oxygen in high
resolution structures of NP4NO doesnt look
spherical
A better approximation to the scattering is needed
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Anisotropic thermal parameters use a symmetric 3
x 3 tensor (six variable parameters) to describe
the probable position of the atom. Instead of
The form of the thermal parameter is
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Anisotropic thermal parameters use a symmetric 3
x 3 tensor (six variable parameters) to describe
the probable position of the atom. Instead of
The form of the thermal parameter is
The result is to describe the atomic position as
a probability ellipsoid, like this
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The result is to describe the atomic position as
a probability ellipsoid, like this
So, why not do this all the time? This
description requires 9 parameters / atom (x,y,z,
6 for the thermal ellipsoid) instead of the
normal 4 parameters / atom (x,y,z, B) At
resolutions less than x.x A, there are not enough
observations to be able to refine anisotropic
thermal parameters? What is x.x?
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The result is to describe the atomic position as
a probability ellipsoid, like this
So, why not do this all the time? This
description requires 9 parameters / atom (x,y,z,
6 for the thermal ellipsoid) instead of the
normal 4 parameters / atom (x,y,z, B) At
resolutions of x.x A, are there enough
observations to be able to refine anisotropic
thermal parameters? What is x.x? 2 Å - No

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The result is to describe the atomic position as
a probability ellipsoid, like this
So, why not do this all the time? This
description requires 9 parameters / atom (x,y,z,
6 for the thermal ellipsoid) instead of the
normal 4 parameters / atom (x,y,z, B) At
resolutions less than x.x A, there are not enough
observations to be able to refine anisotropic
thermal parameters? What is x.x? 2 Å - No
1 Å - Yes

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The result is to describe the atomic position as
a probability ellipsoid, like this
So, why not do this all the time? This
description requires 9 parameters / atom (x,y,z,
6 for the thermal ellipsoid) instead of the
normal 4 parameters / atom (x,y,z, B) At
resolutions less than x.x A, there are not enough
observations to be able to refine anisotropic
thermal parameters? What is x.x? 2 Å - No
1 Å - Yes
1.4 -gt 1.7 Å ????
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Ts.dUMP.PDDF 1.4 Å resolution P63
model R Rfree extra
paramters isotropic .169 .191 0 anisotropi
c .155 .181 26135
Y94F 1.6 Å resolution, I213
model R Rfree extra parameters isotropic .196 .
221 0 anisotropic .175 .208 12290
Is anisotropic refinement justified? (Hint I
wouldnt be leading you down this path if there
werent a third answer.)
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An anisotropically refined structure of a
chromium ligand Atoms in central ring are well
ordered and approximately spherical Atoms in OCH3
groups have large, correlated thermal
motions Can we deduce what the rigid body motion
is from the anisotropic Thermal parameters?
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T(ranslational)L(ibrational)S(crew) analysis
Model of rigid body motion - 20 parameters per
TLS group translation (6 parameter symmetric
tensor) libration (6 parameter symmetric
tensor) screw (nonsymmetric tensor, 8 variable
parameters 1 arbitrary) The screw motion is due
to (a) possible coupling of the translation and
libration motions, and (b) lack of
symmetry. Initially TLS parameters were
determined by fitting anisotropic thermal
parameters. For the example given above
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Top figure shows refined Thermal ellipsoids (36
parameters per OCH3) Bottom figure
shows Thermal ellipsoids Calculated from TL
analysis (20 parameters per OCH3)
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Introduction to Thymidylate Synthase
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Thymidylate synthase catalyses the conversion of
deoxyuridine monophosphate to thymidine
monophosphate by methyl transfer from
5,10-methylenetetrahydrofolate. The protein
undergoes a conformational change upon binding
both substrates. (Montfort, ancient
history) (show protein in coot)
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Thymidylate synthase catalyses the conversion of
deoxyuridine monophosphate to thymidine
monophosphate by methyl transfer from
5,10-methylenetetrahydrofolate. The protein
undergoes a conformational change upon binding
both substrates. (Montfort, ancient
history) (show protein in coot)
The figure at rights shows which segments move
when ligands bind Can we learn something
about the conformational change from TLS analysis
of the protein? Answer Right now, I dont know.
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How does one determine appropriate TLS
groups? 1. guess
In some cases this is remarkably effective You
can divide the protein a) not at all b) into
domains c) into subunits
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How does one determine appropriate TLS
groups? 1. guess 2. UW server http//skuld.bmsc
.washington.edu/tlsmd/index.html (show results
movement) jobs/TLSMD234/ANALYSIS/index.html
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How does one determine appropriate TLS
groups? 1. guess 2. UW server http//skuld.bmsc
.washington.edu/tlsmd/index.html (show results
movement) 3. ESCET (Thomas Schneider) Escet
determines conformationally invariant regions of
a protein by comparing two structures and
determining if the differences are statistically
significant (using esds from maximum
likelihood. ESCET was run (a year ago) with
open/closed TS structures (I have to do this
again w/ better resolution structures)
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Escet output white regions are invariant
(within error) red - expansion blue -
contraction use this to determine parts of the
structure which are invariant and parts which
move together (show conserved residues in
structure)
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Apply TLS analysis to TS
Ts.dUMP.PDDF 1.4 Å resolution P63
model R Rfree extra
paramters isotropic .169 .191 0 anisotropi
c .155 .181 26135 TLS-5 .163 .185 200 TLS-20 .1
60 .182 800 TLS-escet .163 .185 200 (large core)
Y94F 1.6 Å resolution, I213
model R Rfree extra parameters isotropic .196 .
221 0 anisotropic .175 .208 12290 TLS-5 .181 .20
4 100 TLS-10 .179 .202 200 TLS-20 .178 .202 400
The increase in Rfree is comparable to that from
anisotropic refinement - the TLS analysis is as
good (probably better) a model as the anisotropic
model.
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TLS group 1 no T tensor ( 1) -0.113
-0.054 -0.118 -0.021 0.008 -0.021 L tensor
( 1) 1.321 1.241 1.016 0.253 0.018
-0.433 S tensor ( 1) -0.041 -0.044 0.126
-0.153 -0.161 -0.150 0.073 0.214 TLS group
2 m1 T tensor ( 2) -0.097 -0.063
-0.079 -0.056 0.031 0.056 L tensor ( 2)
4.083 9.130 11.748 -0.175 1.144 7.837 S
tensor ( 2) -0.153 0.140 0.087 0.320
0.140 -0.162 -0.181 -0.063 TLS group 3
m2 T tensor ( 3) -0.118 -0.076 -0.103
-0.016 -0.030 0.022 L tensor ( 3) 3.286
2.095 1.452 1.688 -1.238 -0.834 S tensor
( 3) -0.208 0.156 -0.237 0.011 -0.140
0.229 -0.148 0.179 TLS group 4 m3 T
tensor ( 4) -0.137 -0.102 -0.144 -0.005
-0.003 0.006 L tensor ( 4) 1.787 3.564
2.381 1.572 0.980 1.406 S tensor ( 4)
-0.069 -0.030 -0.137 0.000 -0.072 0.052
-0.084 -0.091 TLS group 5 m4 T tensor (
5) -0.024 -0.053 -0.100 -0.034 0.017
0.011 L tensor ( 5) 15.232 17.332 20.126
-4.728 -11.933 16.780 S tensor ( 5) -0.777
0.162 0.111 0.359 0.137 -0.050 -0.202
-0.809
10 - 24 51-117 123-149 261-264
Analysis of last group blows up - Add to group
2? Convert to more reasonable values with TLSANL
(CCP4 - Martyn Winn) (TLSANL will output file
with screw axes for input to molscript)
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Comparison of monomers A and B in a TS ternary
complex structure
core 10-24 51-117 123-149 261-264
monomer B is less ordered than monomer A (no
surprises)
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Conclusions Is this useful for TS? Not yet
able to tell Is this useful in general? Yes -
if for no other reason than to lower R Note
Analysis of a 2.75 Å structure (Ts-NO2dU) with
5 TLS groups gives results that arent
out of line with those from 2-ish Å
structures. Analysis with 20 TLS
groups failed..