Biomedical Engineering Reference
In-Depth Information
[Figure 9.4(C)]. Using such a Monte Carlo based approach, several iterations
are carried out until convergence is reached, defined as achieving agreement
with the measured RDCs exceeding the experimental error. The ensemble size
is then incrementally increased in steps from N 5 1 until convergence is
reached. Using this approach, with a starting MD-generated conformation
pool of 80 000 TAR structures, an ensemble of 20 conformers was determined
that agreed to near-within experimental error with measured RDCs (RMSD 5
4.8 Hz compared to experimental error y4 Hz).
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Approaches have also been developed to use RDCs in reconstructing
smooth continuous motional paths.
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In one approach, the time-averaged
Wigner elements are expressed in terms of a four-dimensional quaternion q(u)
representing the relative orientation of two chiral fragments as a single-axis
rotation from which a four-dimensional hypersphere can be defined. On this
hypersphere, the quaternion can be further expressed as a line integral over a
curve in configuration space which contains a heterogeneous ensemble of
equally weighted conformations. The curve is approximated using a series of
geodesic segments, and the resultant weights of different conformations are
proportional to the number of times the path visits that particular
conformation. With this approach, the authors showed that the measurement
of RDCs under five alignment conditions can be used to reconstruct salient
features of a multi-segment inter-helical motional trajectory corresponding to
an MD simulation of TAR RNA.
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It is important—and often not trivial—to independently assess any dynamic
ensemble or motional model generated using RDCs. Several strategies can be
used. First, part of the RDC data can be omitted from the dynamics analysis
and reserved until the end to evaluate the constructed dynamics.
86,145,146
However, care should be taken in selecting which RDCs to exclude and
ensuring that they correspond to regions that have other RDCs to help define
structural dynamics. One could use an independent set of RDCs, such as those
that can be obtained using field-induced alignment and for which the overall x-
tensor for a given candidate conformer can be predicted based on structure.
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Second, the constructed dynamics can be interrogated with other NMR
measurements, including NOEs and NMR probes of hydrogen bonding. For
example, in the analysis of the generated TAR dynamic ensemble, the flexible
bulge residue U23 is frequently stacked on helical residue A22, consistent with
an NOE cross-peak observed between these two bases, and the flexible A22-
U40 base pair rarely formed the expected WC hydrogen bond geometry,
consistent with the severe line broadening of the U40 imino proton.
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9.5.5 Explicit Treatment of Motional Couplings
All of the above approaches assume that the internal and overall motions are
not correlated to one another. What happens when this approximation breaks
down? Considering such correlations requires the ability to predict the overall
alignment/order tensor based on the structure of an RNA conformer. As
