Biomedical Engineering Reference
In-Depth Information
9.3.2 Magnetic-Field-Induced Alignment
Another method for aligning nucleic acids involves spontaneous alignment
from interactions with the magnetic field itself.
35,52
Some of the first studies
measuring anisotropic interactions of biomolecules relied on the spontaneous
field alignment of molecules with large magnetic susceptibility anisotropies
(Dx), with nucleic acids as well as paramagnetic proteins being primary
targets.
20,35,52,79,80
In nucleic acids, the diamagnetic susceptibility primarily
originates from the aromatic nucleobases, in which the circulation of p-orbital
electrons in response to the magnetic field creates an induced dipole moment,
which then re-interacts with the magnetic field, causing an anisotropic
preference in the molecular orientation [Figure 9.2(B)]. The degree of
alignment depends on Dx as well as the square of magnetic field strength (B
0
).
While the magnetic susceptibilities of individual bases are not adequate to
induce a useful degree of alignment (ca. 2-7 6 10
26
at 800 MHz field
strength), their constructive addition, particularly in helices in which bases are
nearly co-axially stacked, enhances the total anisotropy and resulting degree of
order (typically 10
24
at 800 MHz). Importantly, the net principal x-tensor
direction (x
zz
) need not be coincident with the long axis of the molecule, and
therefore the S
zz
direction, providing a useful approach for measuring a second
independent RDC data set.
75,77,81
Unlike the phage-ordering medium, which
typically orients RNA such that the long axis is on average oriented along the
magnetic field, the diamagnetic alignment of nucleic acids is generally negative
(x
zz
,0) with the x
zz
direction being, on average, oriented perpendicular to the
magnetic field [Figure 9.2(B)] although under certain conditions it is possible
to have conformations with positive alignment (x
zz
.0).
For magnetic-field-induced alignment, the order tensor elements can be
expressed in terms of the magnetic field strength (B
0
), the x-tensor (in units of
m
3
per molecule), and temperature (T)
34,35,40,44
:
and S
xx
{S
yy
~dx
,
B
0
15m
0
kT
B
0
10m
0
kT
S
zz
~Dx
ð
9
:
4
Þ
where
and dx~x
xx
{x
yy
:
x
xx
zx
yy
2
Dx~x
zz
{
ð
9
:
5
Þ
Field-induced RDCs are obtained by measuring splittings at several
magnetic field strengths, preferably three or more. Splittings are plotted as a
function of B
0
to back-calculate isotropic scalar couplings (J), i.e., splittings at
zero field. RDCs at a given field strength, typically the highest field, are then
calculated by subtracting J from observed splittings (J + D). Apparent field
RDCs can be measured from the difference in splittings at only two magnetic
fields; however, eqn (9.5) must be adjusted accordingly.
82
