Biomedical Engineering Reference
In-Depth Information
experiment enables calculation of the paramagnetic effect since
C
2
~R
2,para
{R
2,dia
, enabling subsequent determination of the distance to the
paramagnetic centre. The required transverse relaxation rates are either
obtained from the linewidths in 2D HSQC or TROSY experiments or through
direct measurement of the transverse relaxation rate constants.
194,195
The PCS effect arises from the attachment of a paramagnetic lanthanide ion,
which has an anisotropic contribution to the x-tensor, and manifests as large
changes
in
the
chemical
shifts
of
nuclei
exposed
to
the
paramagnetic
lanthanide.
The
change
in
chemical
shift
between
the
diamagnetic
and
paramagnetic samples is described by the equation:
193
1
12pr
3
3
2
Dx
rh
sin
2
hcos2w
Dd
PCS
~
Dx
ax
(3cos
2
h{1)z
ð
12
:
2
Þ
where Dx
ax
and Dx
rh
are the axial and rhombic components of the magnetic
susceptibility tensor of the ligated metal, and h and w are the spherical polar angles
of a nucleus with respect to the principal axes of the magnetic susceptibility tensor
as located on the paramagnetic metal. PCS are through-space interactions,dueto
the dipolar effect, and as a result of the r
23
term, occur over much greater
distances compared to the PRE effect, typically up to 40
˚
. This has the significant
advantage that the PCS effect can be observed for nuclear spins that are
unaffected by the PRE. The shift effect can be observed simply in [
1
H,
15
N] HSQC
spectra with the
1
Hand
15
N nuclei affected similarly by the PCS, facilitating
reassignment of the paramagnetic spectrum.
196
The additional dependence on the
angular orientation of the nuclei to the magnetic susceptibility tensor make PCS-
derived information potentially more valuable than PRE-based restraints.
Metals with an anisotropic magnetic susceptibility will align in the static
magnetic field B
0
, leading to the observation of RDCs, providing information
about the orientation of dipolar-coupled spin pairs relative to a molecular
alignment tensor. The effect between two nuclei I and S is given by:
193
z
3
D
IS
~
{hB
0
c
I
c
S
3cos
2
h{1
2
Dx
rh
sin
2
hcos2w
240r
I
3
k
B
T p
3
| Dx
ax
ð
12
:
3
Þ
where k
B
is the Boltzman constant; T is the temperature; and h and w are
spherical polar angles of the internuclear vector, relative to the principal axes
of the molecular alignment tensor. Use of RDCs as a structural restraint is
discussed further below (Section 12.5.2).
In order to observe the effects of the interactions outlined above, a
paramagnetic centre must be introduced into the protein: To measure the PRE
effect alone, spin-labels, such as the nitroxide labels MTSSL (paramagnetic)
and the diamagnetic reference ATSSL
197
can be attached to cysteines in a
protein. In the case where a protein contains multiple cysteines, these must be
mutated in order to ensure that the tag is added at a single site, which may
cause complications if disulphide bonds are an integral part of the structure. In
