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 <i>Q</i> observable by NMR, such as NOE intensities or ³<i>J</i>-couplings, for which a relation <i>Q</i>(<i>r</i>) between the quantity <i>Q</i> and a single structure <i>r</i> of a protein can be used to calculate average values ⟨<i>Q</i>(<i>r</i>)⟩, 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 ³<i>J</i>-couplings.