Biomedical Engineering Reference
In-Depth Information
alignment of nucleic acids; additionally, it is generally more difficult to
measure the required number of spatially independent RDCs to simulta-
neously determine both internal and overall tensor parameters. As mentioned
above, this type of analysis also assumes that internal and overall motions are
not correlated to one another, which does not always hold in highly flexible
RNA
molecules,
although
domain
elongation
approaches
overcome
this
problem
71
(see Section 9.5.2).
In principle, much more dynamics information can be obtained from
analysing collections of five or more spatially independent RDCs measuredin
a semi-rigid chiral fragment, such as an A-form helix in RNA.
122,123
Here, one
can use the RDCs to determine all five elements of a time-averaged order
tensor ST
k
T
l
[Figure 9.4(A)] describing the alignment of a fragment relative to
the magnetic field, which can in turn be expressed in terms of the overall
alignment tensor of the molecule and time-averaged Wigner rotation elements,
SD
nk
(abc)T:
29
ST
k
T
l
~
X
X
2
2
O
2
m
(PAS)
l
D
2
mn
(h
l
)SD
nk
(abc)T
ð
9
:
7
Þ
m~{2
n~{2
Here, all 25 SD
nk
(abc)T({n,k}522, 21, 0, 1, 2) time-averaged Wigner
elements (Table 9.3) can theoretically be determined, provided the measure-
ment of RDCs and the five elements of ST
k
T
l
under five linearly independent
alignment conditions.
29
These 25 time-averaged Wigner elements represent the
theoretical maximum dynamic angular information due to internal motions
that can be obtained from RDCs.
29
Here, the sensitivity extends to all three
Euler angles, including a, as well as co-variations between them, given the
simultaneous dependence of many Wigner terms on all three Euler angles.
29,71
The above approach is well suited to analysing RNA chiral helices and 9 out of
25 Wigner elements have been experimentally determined in the TAR RNA
system by using the domain elongation strategy.
71
The measurement of all 25
Wigner elements in RNA remains to be an important challenge for the future
which will require robust methods for varying alignment.
9.5.2
Decoupling Internal and Overall Motions by Domain
Elongation
As described above, the interpretation of RDCs in terms of internal motions
often hinges on the assumption that the internal and overall motions are not
correlated to one another. This makes it possible to separate averaging
contributions due to internal motions from the much larger effects arising due
to overall motions.
23,50,58
Indeed, most formalisms developed in studies of
protein dynamics invoke this so-called 'decoupling approximation'. In
practice, this decoupling approximation can break down in highly flexible
RNA systems. Here, collective motions of A-form helical domains about
