Ultrahigh Resolution Characterization of Domain Motions and Correlations by Multialignment and Multireference Residual Dipolar Coupling NMR

Nuclear magnetic resonance (NMR) residual dipolar couplings (RDCs) provide it unique opportunity for spatially characterizing complex motions in biomolecules with time scale sensitivity extending up to milliseconds. Up to five motionally averaged Wigner rotation elements, < D-0k(2)(alpha beta)>, can be determined experimentally using RDCs measured in five linearly independent alignment conditions and applied to define motions of axially symmetric bond vectors. Here, we show that up to 25 motionally averaged Wigner rotation elements, < D-mk(2)(alpha beta gamma)>, can be determined experimentally from multialignment RDCs and used to characterize rigid-body motions of chiral domains. The 25 < D-mk(2)(alpha beta gamma)> elements form a basis set that allows one to measure motions of a domain relative to an isotropic distribution of reference frames anchored on a second domain (and vice versa), thus expanding the 3D spatial resolution with which motions can be characterized. The 25 < D-mk(2)(alpha beta gamma)> elements can also be used to fit an ensemble consisting of Lip to eight equally or six unequally populated states. For more than two domains, changing the identity of the domain governing alignment allows access to new information regarding the correlated nature of the domain fluctuations. Example simulations are provided that validate the theoretical derivation and illustrate the high spatial resolution with which rigid-body domain motions can be characterized using multialignment and multireference RDCs. Our results further motivate the development of experimental approaches for both modulating alignment and anchoring it oil specifically targeted domains.