Chemistry Reference
In-Depth Information
-C
0
,are
to H
a
-C
a
bonds. On the other hand, bond lengths for heavy nuclei, e.g., C
a
consistent with values reported from crystallography studies [
50
].
By expressing RDC using Eq. (
3
), where the Saupe matrix is multiplied by bond
directional cosines within a local molecular frame, we assume protein conforma-
tional change does not affect the alignment tensor. Thus Eq. (
3
) is an approximation
to Eq. (
2
), in which the average bracket over the second order Legendre polynomial
is applied. This approximation is valid when RDCs from the structured part of the
proteins are analyzed. For small proteins GB3 [
41
,
51
] and ubiquitin [
52
] the model
free (MF) order parameter from
15
N spin relaxation analysis and the order parame-
ter derived from RDC analysis were strongly correlated. These indicate that the
effect of slowmotion dynamics on microsecond to millisecond time scales on RDC
may be negligible and a single structure representation is sufficient for the
structured part of proteins within the current experimental uncertainty [
53
].
When the dynamics involve large scale amplitudes of motion, e.g., the MF order
parameter
S
2
0.6, multiple structures may exist and each one of them is subjected
to its own alignment tensor that may vary significantly due to different steric, and
electrostatic interactions of each conformer to the alignment media. Specifically for
unfolded proteins it becomes challenging to separate intrinsic bond dynamics from
Saupe order parameters in the laboratory frame because local motion and the
overall perturbed diffusive motions are coupled [
54
]. Monte-Carlo simulation of
an ensemble of conformers and the following comparison to measurements remain
the only option to interpret RDCs in a flexible system [
55
,
56
]. The application of
RDCs to study protein in an unfolded state is an active research field [
57
-
59
]. For
instance, efforts have been made to represent the conformational space of urea
denatured ubiquitin with as few as 200 conformers, which seem to reproduce
measured RDCs [
59
]. However, additional specific bond type RDC scaling factors
had to be applied for H-N, H
<
, etc., which indicate different amounts of motion
along bond vectors within a peptide plane [
57
,
59
].
a
-C
a
4.2 Common Applications of RDC
The most common use of RDCs is for structure validation and refinement. Given
structure coordinates determined either from X-ray crystallography or solution
NMR, one can readily fit RDC data to the corresponding bond vector directions
within the molecular frame. Any programs that utilize Eqs (
3
)or(
5
) in a chi-square
minimization routine or formal software packages such as PALES [
60
,
61
] and
REDCAT [
62
] which implement the SVD algorithm can be employed to carry out
the numerical fitting. The fitting will result in the optimized alignment tensor and
values that best matched the measured RDCs. To quantify the agreement between
a structure and measured dipolar couplings, Cornilescu et al. [
63
] proposed quality
factor
Q
. This factor can better determine the quality of the fit than Pearson's
correlation
R
. Shown in (
8
) is the expression for the
Q
factor where rms refers to
root mean square. It provides an estimate of average disagreement in percentage
