Graphical analysis of the relative orientation of molecular alignment tensors for a protein dissolved in two...

In order to determine precise three-dimensional structures of proteins by residual dipolar coupling constants as the major or even exclusive structural constraints, it is essential to use two anisotropic media. In doing so, a reliable and versatile method for estimating the relative orientation of the alignment tensors for the molecules dissolved in different anisotropic media is required. In this communication, we present a new graphical approach for this purpose, which does not require structural information of the target molecules. The correlation map for the two independent data sets of residual dipolar coupling constants, which can be obtained for the molecules in different anisotropic media, strongly depends on the relative orientation of the alignment tensors. We have simulated the correlation maps for all possible combinations of the Euler angles, which transform one alignment tensor to the other, and compared them to the experimental data sets reported for labeled human ubiquitin. This simple graphical method affords a useful starting point for the structural determinations using residual dipolar couplings.