Biomedical Engineering Reference
In-Depth Information
mechanism for isotropic paramagnetic centers such as nitroxide radicals,Mn
2+
and Gd
3+
. This form of PRE is proportional to c
I
2
,so
1
H is the most sensitive
of the commonly observed nuclei; however, observing nuclei with a smaller
ratio such as
13
Cor
15
N can be helpful to counteract extreme line broadening
to obtain structural data nearer the paramagnetic center. For those nuclei, the
effects cannot be observed as far away from the center as for
1
H nuclei.
7,78,79
PRE is also caused by the Curie mechanism,
80
for which the transverse
relaxation rate, R
2,Curie2spin
, is defined by eqn (6.5):
8
2
v
2
g
4
m
B
S
2
Þ
2
R
2,Curie{spin
~
1
5
m
0
4p
Sz1
3t
r
1zv
I
t
r
ð
4t
r
z
ð
6
:
5
Þ
(3kT )
2
r
IM
Curie-based PRE occurs with anisotropic paramagnetic metal ions such as
lanthanides, but it is dependent only on the isotropic components of the x-
tensor.
80
This type of PRE depends on t
r
, not on t
s
, and it scales with v
2
.
Thus, it becomes important for large proteins and at high magnetic field
strength. Incidentally, the R
1,Curie2spin
relaxation is negligible.
4
Note that both
forms
r
IM
26
,
of
PRE
are
proportional
to
making
them
highly
distance
dependent and therefore particularly sensitive to invisible states.
In the presence of a paramagnetic center, the coupling of the free electronsto
nuclei will increase both the longitudinal and transverse relaxation rates. PRE
can be measured using either, but R
2,para
is easier to measure accurately. It is
also less susceptible to internal motions and cross-relaxation than R
1,para
.
36
R
2,para
has traditionally been determined using peak intensities, which are
measured by peak height, in HSQC spectra of diamagnetic (I
dia
)and
paramagnetic (I
para
) samples at a single time point according to eqn (6.6):
I
dia
~
R
2,dia
e
({R
2,para
t)
I
para
ð
6
:
6
Þ
R
2,dia
zR
2,para
where R
2,dia
is the transverse relaxation rate for the diamagnetic sample,
measured as half the peak width at half height, and t is the period in which the
1
H magnetisation experiences transverse relaxation during the pulse
sequence.
22
Once acquired, the experimental PRE data can be transformed
into structural restraints for ensemble modelling.
36
A single-time-point method can underestimate R
2,para
when a short
repetition delay is used because the magnetisation paramagnetic sample
recovers faster than in the diamagnetic sample due to the PRE effect on R
1,para
.
Therefore, a two-time-point measurement has also been proposed
81
in which
R
2,para
can be obtained from eqn (6.7):
1
T
b
{T
a
ln
I
dia
(T
b
)I
para
(T
a
)
I
dia
(T
a
)I
para
(T
b
)
R
2,para
~
ð
6
:
7
Þ
where T
a
is the initial time (T
0
) and T
b
is a second time point at T
0
+ DT. This
