Biomedical Engineering Reference
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describes the structural rigidity and amplitude of helical motions, while h describes
the directionality of those motions.
The method described is limited by the 4 n −1 degeneracy of the order tensor solu-
tion (Tolman and Ruan 2006 ) , where n is the number of independent rigid helical
domains that need to be oriented to each other. While this degeneracy can some-
times be partially overcome by covalent connectivity, steric clash, or experimental
restraints (Bailor et al. 2007 ), it may be challenging to determine the correct orienta-
tion for RNAs with more than two domains (Zuo et al. 2008 ) . Additionally, domain
motions can occur on the same timescale as overall rotational motions (Dethoff
et al. 2009 ), which convolutes dynamics analysis. One way to decouple domain
motions from the overall reorientation of the molecule is through RNA helical
extension (Zhang and Al-Hashimi 2009 ) such that the domain motions occur on a
different timescale from the overall rate of molecular tumbling.
The dynamics of the HIV-1 transactivation response (TAR) RNA (Al-Hashimi
et al. 2002 ; Pitt et al. 2004 ; Zhang et al. 2006 ; Casiano-Negroni et al. 2007 ) has been
extensively studied using RDCs. Located in the 5¢ end of all HIV-1 pre-mRNA tran-
scripts (Muesing et al. 1987 ), the TAR hairpin regulates viral replication (Frankel
1992 ) through its interaction with the trans-activator protein (Tat) (Cullen 1986 ) .
Al-Hashimi et al . demonstrated that in low salt conditions TAR has an average inter-
helical bend angle of 47° and moves with isotropic motions sampling all positions
within a cone radius angle of 46° (Al-Hashimi et al. 2002 ). In the presence of mag-
nesium chloride and increasing concentrations of sodium chloride, TAR's dynamic
motions are quenched and the RNA linearized (Pitt et al. 2004 ; Casiano-Negroni
et al. 2007 ) .
For the HIV-1 TAR RNA, using elongated-helical domains to study RNA dynam-
ics yielded residue-specific measurements of internal motions in TAR that were not
apparent using the smaller, non-elongated RNA (Zhang et al. 2006 ) . Molecular
dynamics and order tensor analysis were further combined to trace out the entire
helical trajectory for TAR where the helices bend and twist in a correlated manner
(Frank et al. 2009 ). These studies of TAR demonstrate the utility of using NMR to
study RNA dynamics.
8.1.3
RNA Structure Analysis by Small Angle X-Ray Scattering
Many RNA structures important for translational control of gene expression are
large by NMR standards, making structure determination quite challenging and
expensive. Fortunately, SAXS is a complementary technique for extracting global
shape information about macromolecules in solution. SAXS also provides a method
for monitoring the kinetics of macromolecular folding in real time and can be used
to assess and compare the solution state conformation of molecules to structures
determined by X-ray crystallography and cryo-electron microscopy. Because
SAXS alone provides low resolution structural information, the combination of SAXS
with an NMR-based approach is ideal for characterization of large RNA molecules
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