Chemistry Reference
In-Depth Information
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2 Theoretical Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3 Alignment Methods .......................................................................... 52
3.1 Charged Polyacrylamide Gel .......................................................... 53
3.2 DNA Based Media ..................................................................... 53
3.3 Collagen Gel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.4 Composite Media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.5 Conservative Mutation . . . .............................................................. 55
3.6 RDC/RCSA Accuracy Improvement .................................................. 55
4 Interpretation and Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.1 Approximations ........................................................................ 57
4.2 Common Applications of RDC ....................................................... 58
4.3 Ensemble Minimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.4 Structure of a Ligand in a Bound State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.5 Structure of Oligomeric State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
1
Introduction
Solution NMR spectroscopy is a powerful technique to study protein structure and
dynamics at the atomic level. The method relies on a variety of experimental
restraints to determine protein structure. These include the nuclear Overhauser
effects (NOEs) that provide interproton distances, the
J
-coupling constants that
depend on dihedral angles [
1
-
3
], the paramagnetic relaxation enhancement (PRE)
that is distance dependent with respect to the paramagnetic center [
4
], and the
residual dipolar couplings (RDC) that report on internuclei vector orientations.
NOE typically measures interproton distances of less than 5
˚
and
J
-coupling
probes spin nuclear interactions within a few bonds away and they are therefore
local in nature. In contrast, PRE can measure distances up to 20-30
˚
from the
paramagnetic center. In this respect RDC is unique. It can provide relative
orientations among internuclei vectors irrespective of their distance separations.
This unique property of RDC has opened up new possibilities in using NMR to
study phenomena that were previously unattainable.
In the presence of a magnetic field, RDCs arise when the proteins in solution
weakly align relative to the field, thus creating an anisotropic condition. The
direction of the alignment of the protein molecules in the magnetic field is com-
monly referred to as the alignment tensor frame. Under such anisotropic condition,
with the presence of an external field, a magnetic dipole-dipole interaction does not
average to zero and yields a measurable dipolar coupling. The magnitude of the
dipolar coupling depends on the angle between the internuclei vector and the external
magnetic field as well as the internuclei distance. If the dipolar interaction is between
two covalently bonded nuclei, then the internuclear distance is fixed and only the
orientation dependence remains. A typical measurement may report hundreds of
