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protein concentration (~0.1-1.0 mM) the measured RDC would primarily reflect
the dimer structure. The crystal structure of YkuJ is a tetramer and there are two
possible configurations for a dimer structure. Wang et al. [ 83 ] aligned the protein
using two alignment media, 5% poly(ethylene glycol)/hexanol and 10 mg/mL
phage Pf 1. Both yielded different alignment tensor directions. However, the
x axes from the two tensors were close to each other and were believed to be the
symmetric axis of the dimer. The further rotation and docking procedure with
energy minimization yielded dimer structure very close to one possible dimer
structure observed in the crystal structure of the tetramer. Prestegard and colleagues
further extended this approach to study structures of weakly associated dimer. The
Staphylococcus epidermidis proteins SeR13 weakly dimerize at a K d on the order
of 10 3 M[ 84 ]. The measured RDCs were the weighted average of monomer and
dimer states and the resulting alignment tensor from direct fitting would be the
average of both monomer and dimer alignment tensors. Lee et al. [ 84 ] circum-
vented this by deriving the exact K d value from concentration dependent chemical
shift values, then extrapolating the RDCs as a function of protein concentration
together with the K d to yield pure RDC data set for the dimer. The rest of the work
to determine the dimer structure was similar to the previous approach [ 83 ], but
with the additional restraints from chemical shift perturbation and paramagnetic
surface perturbation data that helped identifying newly buried surface residues
upon dimerization.
5 Conclusion
Some additional reviews [ 11 , 65 , 87 ] can be found on RDC topics with different
emphasis such as methods [ 69 , 88 , 89 ], theories [ 13 , 14 , 90 ], and dynamics [ 15 ].
In this chapter we have briefly summarized the theoretical expressions for the
widely used RDCs and common descriptions for magnetic alignment under either
Saupe order matrix or alignment tensor representations. RDCs have become nota-
bly more relevant in solution structure and dynamics studies for larger system due
to the fact that the number of NOEs diminishes. In some cases RDCs may be the
sole major experimental NMR restraints for determining domain positions in large
systems of over 100 kDa [ 8 ]. With its essentiality in mind, more alignment media
are being explored. The more choices available, the higher the chance biologically
important proteins and membrane proteins reconstituted in micelles or bicelles can
be aligned without any interference with the media. More RDC measurements on
large and multidomain proteins can reveal their quaternary structure and dynamics
manifested through differences in alignment order. However, caution should be
exercised in RDC data interpretations because a single RDC data set may not be
able to separate differences in domain positions and dynamics simultaneously. Cross-
validating the results with different RDCs under another orthogonal alignment tensor,
rotational diffusion tensors from spin relaxation, and small angle X-ray scattering that
are sensitive to the protein overall shape should help overcome this problem.
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