Biomedical Engineering Reference
In-Depth Information
relative to the other—can be obtained by superimposing their order tensor
frames.
59,60,134
The latter amounts to insisting that helical fragments share, on
average, a common view of the magnetic field direction when assembled into a
proper structure—similar to how countries in a properly assembled map report
to a common compass bearing. The five independent parameters of the order
tensor can be compared for various helices to obtain information about
relative helix motions over sub-millisecond timescales.
59
While helices will
report identical parameters when they are held rigid relative to one another,
inter-helix motions can lead to differences. Specifically, the q value for a given
helix will be attenuated relative to the value observed for a helix that more
strongly dominates total alignment, with the degree of attenuation generally
increasing with motional amplitudes. By taking the ratio of the q values for
each helix (q
HI
/q
HII
5 q
int
), where q
int
ranges from 0 to 1 with 0 having
maximum and 1 having minimum motions, the degree of internal motions can
be determined. Although often difficult to determine reliably, the asymmetry
parameter (g) can provide insight into the directionality of inter-helix motions
with spatially isotropic (directionless) motions having a smaller effect on the
relative helix g values compared to anisotropic (directional) motions.
59,135
Order tensor analysis of RDCs assumes that one fragment dominates overall
molecular alignment of the RNA.
59,85,135,136
As discussed above, this
'decoupling limit' is readily satisfied in elongated RNA molecules or when
helices are held rigidly together. Two other regimes can be identified. In the
extreme coupling limit, helices have similar size and shape and contribute
equally to overall alignment. Here, similar degrees of order may be observed,
even in the presence of inter-helical motions, and the observation of q
int
5 1 does
not rule out the presence of inter-helix motions. Note that depending on the
nature of inter-helical motional trajectory, different q values may be observed
even if the helices have equivalent size and shape. For example, twisting around
the axis of a given helix will result in a reduction of its q without affecting the q
value observed in an adjoining helix. In the intermediate coupling limit, one helix
partially dominates overall alignment and the measured q
int
value will
underestimate the real motional amplitudes.
137
Note that differences on the
order of three base pairs can be sufficient to take an RNA system outside the
extreme coupling limit and into the intermediate regime.
78
9.5.4 Constructing Dynamic Ensembles
Another approach for obtaining atomic-level information regarding RNA
dynamics involves using RDCs to construct dynamic structure ensembles. This
was first demonstrated by Clore and co-workers who analysed RDCs
measured in ubiquitin to create a two-state ensemble
138
and then subsequently
applied the same approach in the determination of a four-state ensemble of
DNA.
139
Alternatively, approaches have been developed in which RDCs are
used to guide selection of conformers from a conformational pool generatedby
