Biomedical Engineering Reference
In-Depth Information
Figure 8.2
Gaussian axial fluctuation (GAF) model of peptide plane re-orientation
(right) showing the three axes about which the amplitude of diffusive
motions is determined in RDC-based GAF approaches. Left: illustration
of how orientational sampling averages differently with respect to
different molecular alignment tensors. The three spheres show the range
of RDC values from large positive for three differently oriented tensors,
emanating from differently aligning media. Adapted from ref.
84
with
permission. # American Chemical Society, 2011.
of streptococcal protein G (GB3).
63
In an initial approach, the average
positions of the backbone heavy atoms were represented by the high-resolution
X-ray structure, and alignment tensors were defined from RDCs associated
with the least dynamic bond vectors identified from an initial analysis. Each
average coupling is then calculated as a function of the amplitude of motions
about the three axes (s
a
, s
b
and s
c
) using:
SDT
3D-GAF
D
max
~
(
)
ð
8
:
3
Þ
r
4p
5
r
R SY
2
3
8
SY
0
Þ
T
3D-GAF
z
Þ
T
3D-GAF
zSY
2
{2
Þ
T
3D-GAF
ð
h
i
,w
i
ð
h
i
,w
i
ð
h
i
,w
i
where
SY
m
h
i
,w
i
Þ
T
3D-GAF
~
ð
<
:
e
{l'
2
s
c
2
e
{i(l''{m)w
z
d
l', m
{h
z
=
;
ð
Þ
d
l'',l'
h
ð
|
e
{n'
2
s
b
.
2
e
{i(n''{l'')w
y
d
n',l''
{h
y
8
<
:
9
=
;
X
2
d
n'',n'
h
y
|
P
2
l',l''~{2
P
2
n',n''~{2
e
{m'
2
s
a
=
2
e
{i(m''{n'')w
x
d
m'',m'
{h
x
Þ
d
m'',m'
h
ð
Y
m''
h
0
,Q
0
ð
ð
Þ
m',m''~{2
ð
8
:
4
Þ
