Chemistry Reference
In-Depth Information
structural information, i.e., paramagnetic resonance enhancement (PRE), pseudocontact
shifts (PCS), and RDC induced by anisotropic paramagnetic centers. In addition, cross-
correlated relaxation (CCR) effects between anisotropic paramagnetic centers and
anisotropic parameters of the nuclear spins can also be exploited to generate long-
range restraints [
19
,
111
,
112
]. Paramagnetic centers with isotropic electron spin
distribution (Mn
2+
and Gd
3+
) produce large PREs due to slow electron relaxation. In
contrast, paramagnetic centers with anisotropic electron spin distribution for most
paramagnetic metal ions, including most of the lanthanides, create all four long-range
paramagnetic effects, which contain rich structural information [
114
]. Here, we will
focus on PRE and PCS and their applications. Information about RDC can be found in
this topic.
The PRE arises from magnetic dipolar interactions between a nucleus and the
unpaired electrons of the paramagnetic center, resulting in an increase in nuclear
relaxation rates. In contrast to NOE, where the effects are limited to short range
interaction (
6
˚
), the PRE effects are relatively large and can be detected up to
35
˚
owing to the large magnetic moment of an unpaired electron. There are two
mechanisms, i.e., the Solomon mechanism and the Curie spin mechanism, that give
the PREs, with the former being predominant for slowly tumbling molecules with
long lifetimes of electronic spin state (such as Mn
2+
and Gd
3+
). However, the Curie
relaxation becomes important when the electronic relaxation is much faster than
the rotational tumbling of the molecules, which is the case for the majority of
paramagnetic metal ions. Theoretical and experimental aspect of PRE as well as its
application in studies of structures of proteins and protein-protein complexes can
be found in recent reviews [
114
-
116
].
At high magnetic fields (over 500 MHz for
1
H frequency), the PRE rate,
<
G
2
,which
arises from the dipole-dipole interaction between a nucleus and unpaired electrons
with an isotopic
g
-tensor, is conventionally calculated by the Solomon-Bloembergen
(SB) equation:
(
)
2
1
15
m
0
4
3
t
c
2
I
g
2
2
r
6
G
2
¼
g
m
B
SS
ð
þ
1
Þ
4
t
c
þ
p
2
1
þðo
H
t
c
Þ
where
r
is the distance between the paramagnetic center and the observed nucleus,
m
0
the permeability of vacuum,
g
I
the nuclear gyromagnetic ratio,
g
the electron
g
-factor,
m
B
the electron Bohr magneton,
S
the electron spin quantum number, and
t
c
the PRE total correlation time. In practice,
G
2
is measured as a difference in
transverse relaxation rates between the paramagnetic (
R
2,para
) and diamagnetic
(
R
2,dia
) states. A two-time point measurement is recommended as a simple approach
for obtaining
G
2
rates and their corresponding errors without fitting procedures. In
this approach, the
G
2
rates are determined from two time points (
T
¼
0 and
D
T
) for
transverse relaxation as shown by the following equation [
116
]:
1
T
b
ln
I
dia
ð
T
b
Þ
I
para
ð
T
a
Þ
G
2
¼
R
2
;
para
R
2
;
dia
¼
T
a
I
dia
ð
T
a
Þ
I
para
ð
T
b
Þ
