Chemistry Reference
In-Depth Information
between measured and calculated dipolar couplings. A
Q
factor of 40%, roughly
corresponding to Pearson's
R
of 0.9, are commonly found on structures with 2-3
˚
resolution; and a
Q
value of 20% or less indicates the structure is at high resolution
(1.5
˚
) and accuracy. Clore and Garrett [
64
] suggested an alternative form
½
1
=
2
to replace the denominator of (
8
) in the case of a limited
RDC sampling over all of the possible orientations. A thorough discussion on
Q
factor can be found elsewhere [
65
].
2
D
a
ð
3
R
2
4
þ
Þ=
5
rms
ð
D
meas
D
calc
Þ
Q
¼
;
(8)
rms
ð
D
meas
Þ
2
E
¼
k
ð
D
meas
D
calc
Þ
:
(9)
For solution structure determination, RDC is normally not included as a poten-
tial term (
9
) during the initial structure calculation in a simulated annealing protocol
in a program such as Xplor-NIH [
66
,
67
]. Due to directional degeneracy associated
with RDC restraints, as described in the theoretical expression section, multiple
local potential minima will hinder the successful search for the right conformation.
Typically a rough tertiary fold of protein is obtained first with the use of NOE
restraints and such a fold can be used as a starting structure for the next simulated
annealing procedure with the combined NOE and RDC restraints. The procedure to
include RDC restraints in a program such as Xplor-NIH uses four pseudo-atoms
(
OXYZ
)[
68
] to represent the alignment tensor directions [
69
]. The RDC force
constant,
k
in (
9
), can be increased gradually as the temperature is being lowered
in the simulated annealing. In the end it is ideal to adjust the force constant
k
so that
the deviation from the measured RDCs matches the experimental error.
4.3 Ensemble Minimization
As discussed before, RDC reflects the ensemble averaged dipolar coupling and
incorporates a wide range of time scales up to milliseconds. During RDC restrained
structure calculations we made approximations by assuming a single conformer. The
question remains whether it is reasonable to keep this assumption in all cases. Clore
and Schwieters [
52
] initially employed a two-member ensemble minimization to test
whether a better agreement between measured and calculated RDC data could be
achieved, and whether it was statistically significant. The ensemble algorithm pro-
posed by Clore and Schwieters [
52
] kept a user-defined number of conformers during
the course of a simulated annealing, and any evaluated physical quantity, e.g.,
D
calc
,is
linearly averaged among individual conformers. After refining the ubiquitin structure
with
D
H-N
data sets collected in 11 different alignment media, and a couple of other
heteronuclear RDCs, they found a single conformer in most cases is sufficient to yield
a good quality factor
Q
less than 20%. The structure was validated against the
D
H
a
-C
a
