Use of Measured Residual Dipolar Couplings to Calculate Residual Dipolar Couplings for a Protein Structure: A Case Study Using Hen Egg-White Lysozyme

Five sets of RDC
values for the backbone of [13C,15N]-labeled
Hen Egg-White Lysozyme (HEWL, 320 RDCs), obtained
from NMR experiments of the protein in an ether bicelle solution at
a temperature of 308 K and pH 3.8, were used to calculate RDC values
by application of two methods, the alignment-tensor (AT) method and
the method of magnetic-field rotational sampling (HRS), applied to
five X-ray structures of HEWL, to investigate the relevance of measured
RDC values for the structure determination or refinement of proteins.
In contrast to other quantities Q observable by NMR,
such as NOE intensities or 3J-couplings,
for which a relation Q(r) between
the quantity Q and a single structure r of a protein can be used to calculate average values ⟨Q(r)⟩, averaged over the Boltzmann-weighted
structural ensemble of the protein at finite temperature in solution,
an RDC is not defined in terms of a single structure but as an average
over a slightly nonuniform rotational and orientation distribution
of the protein. This averaging between large positive and negative
values reduces the kHz size of a dipolar coupling (DC) by a factor
of 103 to 104 to the Hz range of a residual
dipolar coupling (RDC). Since the nonuniform orientation distribution
can neither be measured nor faithfully mimicked at atomic resolution
on a computer, RDC values for a given protein structure are commonly
calculated by minimizing the difference between calculated and measured
RDC values for a given set of measured target RDC values by varying
the orientation distribution of the protein in one way or the other.
These three features of RDCs, a very large reduction of size as a
result of averaging over orientations, their definition in terms of
an unknown, immeasurable orientation distribution, and their calculation
using a set of target RDC values, lead to a sensitivity of the calculated
RDC values to the size and type of the particular set of RDCs used
in the calculation. This reduces the usefulness of measured RDCs for
structure determination or refinement of proteins compared to NOE
intensities or 3J-couplings.