Biomedical Engineering Reference
In-Depth Information
interesting nuclear probes, such as 19 F and 31 P, and important subjects
including interactions with nucleic acids and oligosaccharides, the effects of
chemical exchange, the impact of paramagnetic metal ions, isotope shift
effects, pH titration experiments and temperature dependencies.
3.2 The Chemical Shift Tensor
In the presence of a static magnetic field, the electrons circulating around each
nucleus create electric currents, which in turn induce tiny magnetic fields that
shield nuclear spin magnetic moments from the full effect of the external field.
As a result, NMR frequencies vary depending on the chemical environment
experienced by the nucleus. These induced fields are linearly dependent on the
applied magnetic field, so the resulting 'chemical shift' from a reference
frequency can be represented in the form of a Cartesian tensor with
components along three orthogonal axes. 6 If the vectors B 0 and B ind describe
the applied and induced magnetic fields, then the chemical shift tensor (CST) is
defined by the equation:
0
@
1
A ~d : B 0 ~
0
@
1
A
0
@
1
A
B x ind
B y ind
B z ind
d xx
d xy
d xz
B x 0
B y 0
B z 0
:
B ind ~
d yx
d yy
d yz
:
ð 3 : 1 Þ
d zx
d zy
d zz
The term d zx B z 0 indicates a component of the magnetic field induced in the x
direction by an external field that is applied along the z-direction.
For a static sample, the chemical shift at a particular site will be determined
by the orientation of the molecule relative to the direction of the applied field.
Randomly oriented samples produce broad powder pattern spectra of the sort
shown in Figure 3.1(a), defining the full range of chemical shifts experienced
by the nucleus in question. When uniaxially oriented samples can be prepared,
for example by labelling single backbone amide 15 N sites in a-helices inserted
into planar lipid bilayers that are aligned between glass plates, 7 much narrower
resonances are observed [Figure 3.1(b) and (c)]. The resonance frequencies and
linewidths of such signals can be used to restrain the orientation of peptide
planes relative to the membrane normal, providing valuable information for
structural studies of membrane-associated polypeptides. 8
Macroscopically aligned solid samples are in general difficult to prepareand
the magic-angle spinning methods routinely employed to enhance resolution
sacrifice much of the information about orientation contained in broad line
spectra [Figure 3.1(d)]. Under these circumstances, the residual effectsof
nuclear shielding are described by the isotropic chemical shift d iso , which is
determined by the trace of the CST:
:
1
3
d iso ~
d xx zd yy zd zz
ð 3 : 2 Þ
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