A unifying probabilistic framework for analyzing residual dipolar couplings

Residual dipolar couplings provide complementary information to the nuclear Overhauser effect measurements that are traditionally used in biomolecular structure determination by NMR. In a de novo structure determination, however, lack of knowledge about the degree and orientation of molecular alignment complicates the analysis of dipolar coupling data. We present a probabilistic framework for analyzing residual dipolar couplings and demonstrate that it is possible to estimate the atomic coordinates, the complete molecular alignment tensor, and the error of the couplings simultaneously. As a by-product, we also obtain estimates of the uncertainty in the coordinates and the alignment tensor. We show that our approach encompasses existing methods for determining the alignment tensor as special cases, including least squares estimation, histogram fitting, and elimination of an explicit alignment tensor in the restraint energy.