Application of correlated residual dipolar couplings to the determination of the molecular alignment tensor magnitude of oriented proteins and nucleic acids

Residual dipolar couplings (RDC) between nuclear spins in partially aligned samples offer unique insights into biomacromolecular structure and dynamics. To fully benefit from the RDC data, accurate knowledge of the magnitude (D-a) and rhombicity (R) of the molecular alignment tensor, A, is important. An extended histogram method (EHM) is presented which extracts these parameters more effectively from dipolar coupling data. The method exploits the correlated nature of RDCs for structural elements of planar geometry, such as the one-bond C-13'(i)- C-13(i)alpha, C-13(i)'- N-15(i+1), and N-15(i+1)- H-1(i+1)N couplings in peptide bonds of proteins, or suitably chosen combinations of D-1(C1'H1'), D-1(C2'H2)', D-1(C1'C2)', D-2(C2'H1)', D-2(C1'H2'), and D-3(H1'H2') couplings in nucleic acids, to generate an arbitrarily large number of synthetic RDCs. These synthetic couplings result in substantially improved histograms and resulting values of D-a and R, compared with histograms generated solely from the original sets of correlated RDCs, particularly when the number of planar fragments for which couplings are available is small. An alternative method, complementary to the EHM, is also described, which uses a systematic grid search procedure, based on least-squares fitting of sets of correlated RDCs to structural elements of known geometry, and provides an unambiguous lower limit for the degree of molecular alignment.