7 × 7 RMSD matrix: A new method for quantitative comparison of the transmembrane domain structures in the G-protein coupled receptors

The G-protein coupled receptors (GPCRs) share a conserved heptahelical fold in the transmembrane (TM) region, but the exact arrangements of the seven TM helices vary with receptors and their activation states. The differences or the changes have been observed in the experimentally solved structures, but have not been systematically and quantitatively investigated due to lack of suitable methods. In this work, we describe a novel method, called 7 × 7 RMSD matrix that is proposed specifically for comparing the characteristic 7TM bundle structures of GPCRs. Compared to the commonly used overall TM bundle RMSD as a single parameter, a 7 × 7 RMSD matrix contains 49 parameters, which reveal changes of the relative orientations of the seven TMs. We demonstrate the novelty and advantages of this method by tackling two problems that are challenging for the existing methods. With this method, we are able to identify and quantify the helix movements in the activated receptor structures and reveal structural conservation and divergence as well as the structural relationships of different GPCRs in terms of the relative orientations of the seven TMs.