Biomedical Engineering Reference
In-Depth Information
study described above. The following function was minimised:
2
,
h
i
~
X
ij
i
D
exp
x
2
i,j
{D
calc
d
i,
2
f
h,w,y
g
i
,
fg
j
, S,s
a
,s
b
,s
c
ð
8
:
5
Þ
i,j
where the (h,w,y) describe the mean orientation of plane i, A
j
is the alignment
tensor for medium j, s
a
, s
b
,s
c
and S (order parameter) are the motional
amplitudes that best fit the data for plane i and d
ij
is the estimated weighting of
each RDC dataset. Every peptide plane is treated separately, so that the
approach is 'structure-free' (SF-GAF). Analysis of 'free datasets' removed
from the data set shows a clear minimum in x
?
, which determines the level of
molecular alignment as precisely as possible.
15
N-
1
H
N
order parameters are
compared to those determined using spin relaxation in Figure 8.3, identifying
the presence of increased dynamics in the loop regions of ubiquitin over longer
timescales, and similar amplitude excursions in the regions of secondary
structure of the molecule. The larger amplitude motions in the N-terminal b-
hairpin (8-12) are invisible to spin relaxation because they occur on timescales
slower than the overall tumbling of the molecule (in the range of 4-5 ns). The
distribution of motions found using the SF-GAF approach is very similar to
the distribution found using a model-free approach applied to a dataset
containing only
15
N-
1
H
N
RDCs, although the absolute amplitude of the
motion is much smaller using the SF-GAF approach. This difference is
possibly due to the scaling applied to the model-free-derived data.
49
The only
additional dynamics that should be missed using the SF-GAF approach would
be an equi-amplitude, axially symmetric component that would be common to
all internuclear bonds in the peptide plane for each peptide plane. Data from
each alignment medium were successively removed and two N-H
N
RDCs were
randomly removed from each peptide plane. In both cases RDCs were back-
calculated using static and 3D-GAF models, using appropriate alignment
tensors for the specific models, and the x
2
was significantly lower for the SF-
GAF analysis compared to the static model.
To summarise, RDCs measured in multiple alignment media were analysed
in terms of local backbone dynamics using either model-free approaches, ora
simple models exploiting only shared local structural geometries (e.g., peptide
planes). These methods rely only on experimental RDCs, and can provide
absolute
alignment
tensor
information,
average
coordinates
and
internal
motional modes and amplitudes from experimental data alone.
8.4.2.3
Molecular Dynamics and RDCs
In order to address the physical reality of these results, in terms of the energy
and stability of the protein, it is informative to compare with state-of-the-art
molecular dynamics (MD) technology. A comparison can then be made
between methods that necessarily fit to experimental data, and methods that
rely uniquely on a physically reasonable description of the potential energy
