Chemistry Reference
In-Depth Information
observables mainly reflects values of the spectral density functions at zero,
15
N, and
1
H frequencies, (i.e.,
J
(0),
J
(
o
H
), respectively), the model-free analysis
using the three experimental data sets is suitable to characterize fast internal motion
in proteins [
3
-
5
]. In the model-free analysis, a correlation time for internal motion,
t
i
, is determined for each amide site in addition to
S
2
. Moreover, when the simple
model-free spectral density function is unable to fit the data, an extended model that
contains an order parameter for faster internal motion,
S
f
, an order parameter for
slower internal motion,
S
s
, and a correlation time,
o
N
), and
J
(~
t
s
, for the slower time scale
motion is tested. A chemical exchange term,
R
ex
, is added to test for the presence of
slow (milli- to microsecond) motions as well. These parameter optimizations are
conducted by initially assuming a spherical rigid body rotation of the molecule, i.e.,
assuming a single rotational correlation time,
t
R
. Subsequently, either an axially
symmetric or fully asymmetric model of the molecular rotational diffusion may be
tested. The principles, protocols, and verification of the parameterization derived by
the model-free analysis have extensively been studied and described [
6
-
34
]. In this
section we focus on the recent developments in applying the model-free approach.
2.1 Practical Aspects in
15
N
R
2
Experiment
Since
R
2
is the only observable that provides information about the
J
(0) spectral
density contribution, accurate measurement of this observable is of particular impor-
tance. Transverse relaxation rates are typically measured by either a spin-lock (
R
1
r
)or
a Carr-Purcell-Meiboom-Gill (CPMG) experiment. In the following, advantages and
disadvantages of the two experiments are described with particular consideration of
(1) limitations on the applied
B
1
field strength in which
g
N
is gyromag-
netic ratio of
15
N), (2) off-resonance error, and (3) suppression of cross correlation by
1
H-
15
N dipolar interaction (DD) and
15
NCSA.
o
1
¼ g
N
B
1
(
2.1.1 Spin-Lock
R
1
r
Experiment
In the
R
1
r
experiment, in which relaxation is measured in a rotating reference
frame, an rf field,
B
1
, is applied during the relaxation period, during which time the
magnetization is “locked” almost parallel to
B
1
.
R
1
r
is a function of
R
1
and
R
2
,
given by
R
2
sin
2
R
1
cos
2
R
1
r
¼
y þ
y:
(1)
o
rot
are the Larmor
frequency of the signal and the angular frequency of the rotation frame, respec-
tively. To obtain
R
2
from
R
1
r
most accurately, it is advantageous to increase the
R
2
Here,
y
is given by tan(
o
1
/(
o
0
o
rot
)), and
o
0
and
