A robust method for determining the magnitude of the fully asymmetric alignment tensor of oriented macromolecules in the absence of structural information

It has recently been shown that the degree of alignment of macromolecules in an aqueous dilute liquid crystalline medium of bicelles is sufficient to permit accurate values of residual N-15-H-1, C-13-H-1, and C-13(alpha)-C' dipolar couplings to be obtained on a routine basis, thereby providing potentially unique long-range structural information. To make use of this information in macromolecular structure determination, the magnitude of the axial and rhombic components of the molecular alignment tensor must be determined. This can be achieved by taking advantage of the fact that different, fixed-distance internuclear vector types are differently distributed relative to the alignment tensor. A histogram of the ensemble of normalized residual dipolar couplings for several such vector types approximates a powder pattern from which the magnitude of the axial and rhombic components are readily extracted in the absence of any prior structural information. The applicability of this method is demonstrated using synthetic data derived from four proteins representative of different sizes, topologies, and secondary structures, and experimental data measured on the small protein ubiquitin.