Chemistry Reference
In-Depth Information
15
N-{
1
H} NOE is thought to decrease monotonically as the rate of fast internal
motion increases. However, the actual dependence of the NOE on correlation time
is more complex. For example, when the model-free approach is used to express the
spectral density using a correlation time for internal motion (
t
i
) as well as an overall
t
R
), the NOE is a two-valued function of
t
R
, attaining a maximum
correlation time (
t
R
(for example, see Fig. 19.10 in [
59
]).
value at one value of
3 Extending Relaxation Measurements Beyond
R
1
,
R
2
, and
15
N-{
1
H} NOE
Although a set of
15
N
R
1
,
R
2
, and
15
N-{
1
H} NOE is commonly used to characterize
backbone protein dynamics, other relaxation experiments are also useful to charac-
terize protein dynamics. Use of other than three experimental data allows an
application of a more detail dynamics model than the conventional model-free
model. For example, cross-correlated longitudinal (
XY
) rates
between
1
H-
15
N DD and
15
N CSA have provided useful information about protein
backbone dynamics [
14
,
60
,
61
]. Since cross-correlated relaxation occurs together
with auto-relaxation, the rate is obtained by multiple exponential fitting [
36
,
62
-
65
]. As an alternative approach, the
Z
) and transverse (
XY
rate has been more accurately deter-
mined by taking intensity ratios of the inphase and antiphase magnetization [
66
].
In the analysis of cross-correlated relaxation rates to detect protein dynamics, the
relative orientation between the
15
N-
1
H dipole and the
15
N tensor (
s
k
) is required
as an additional parameter for fitting the data [
67
,
68
]. Numerous measurements of
cross correlated relaxation have been used to estimate the
15
N CSA in protein
backbone in solution [
14
,
15
,
66
,
67
,
69
-
73
]. According to these results,
15
N CSA is
an axially symmetric CSA tensor, 169
5 ppm, with a relative orientation about
21.4
2.3
tilted against the N-H dipolar tensor [
73
]. Thus, a disadvantage of the
use of
XY
is that this tilted angle from the N-H vector has to be included as a fixed
parameter in the model-free analysis. Since the relative contribution of
XY
in
S
2
depends on the degree of internal motion in each residue, use of
XY
may introduce
an additional uncertainty in the model-free analysis. Therefore, it is important to
clarify how much
15
N CSA varies site-specifically.
Recently, relaxation rate products (2N
X
H
X
,2N
Z
H
X
,2N
X
H
Z
, and 2N
Z
H
Z
) have
been measured to extract information about internal motion of proteins [
74
]. By
addition and subtraction of these four terms there ideally remains only the relaxa-
tion rate, that contains the
J
(0) term, obtained by dipolar coupling. Using this
relaxation rate as well as
R
1
and
15
N-{
1
H} NOE values,
S
2
values independent
from the chemical exchange contribution were determined. The same set of data has
also been applied to extract chemical exchange contribution [
75
].
Dynamics on a time scale much slower (i.e., ~10 ms) than can be measured by
R
2
relaxation dispersion is often characterized by measuring the exchange of the
longitudinal
1
H magnetizations among species undergoing chemical exchange
