Biomedical Engineering Reference
In-Depth Information
anisotropic interactions no longer average to zero and residual effects, such as
RDC, can be measured.
3
RDC provides information about the orientation of
bond vectors in relation to the alignment tensor. This information can be used
to refine protein structures or determine the global fold of a protein and
determine orientations of protein domains in combination with few other
data.
55
RDC is measured as an addition to the J-coupling. In the case of
paramagnetic alignment, the RDC is defined as the difference in the coupling
between nuclei in a paramagnetic and diamagnetic sample.
56,57
RDC (D
res
)
provides
particularly
valuable
structural
restraints
because
they
are
not
dependent on the distance to the paramagnetic center [eqn (6.1)]:
D
res
~{
B
0
15kT
c
A
c
B
h
16p
3
r
3
AB
Dx
ax
(3cos
2
H{1)z
3
2
Dx
rh
(sin
2
Hcos2Q)
ð
6
:
1
Þ
where B
0
is the magnetic field strength, k is the Boltzmann constant, T is the
absolute temperature, c
A
and c
B
are the gyromagnetic ratios of nuclei A and B,
h is Plank's constant, r
AB
is the distance between the coupled nuclei, Dx
ax
and
Dx
rh
are the axial and rhombic components of the x-tensor and angles H and Q
determine the orientation of the inter-nuclear vector relative to the magnetic
susceptibility tensor x.
57
The x-tensor is degenerate and multiple values for H
and Q will give the same RDC values.
53
This problem can be solved by
collecting data with different lanthanides,
16,26,32,58
with paramagnetic centers
at different positions
29,59
or by using a second set of restraints such as
PREs
30,52,60-63
or PCS.
58,64-67
6.2.2
PCS Theory
Paramagnetic centers with anisotropic electron distribution cause changes in
the chemical shifts in the NMR spectra, called paramagnetic shifts, resulting
from both through-bond Fermi contact shifts and through-space PCS.
68
Fermi
contact shifts decay rapidly with the number of bonds from the metal and are
generally only used to study ligands bound to the paramagnetic center.
69
Conversely, PCS provide long-range structural information, up to 60
˚
64,70
and their predictable nature makes the data easy to interpret.
71
Chemical shift
anisotropy (CSA) also makes a small contribution to the shift but it can be
corrected for during data analysis.
72
The PCS (d
PCS
) is proportional to the inverse cubic distance between the
nucleus and the paramagnetic center, r
IM
23
[eqn (6.2)].
8
1
12pr
I
3
3
2
Dx
rh
(sin
2
hcos2w)
Dx
ax
(3cos
2
h{1)z
d
PCS
~
ð
6
:
2
Þ
The distance r
IM
and the angles h and w are the polar co-ordinates of the
nucleus in the frame of reference of the x-tensor with its origin at the
paramagnetic center. They are determined experimentally by measuring the
