Analysis of slow interdomain motion of macromolecules using NMR relaxation data

The interpretation of NMR relaxation data for macromolecules possessing slow interdomain motions is considered. It is shown how the "extended model-free approach" can be used to analyze N-15 backbone relaxation data acquired at three different field strengths for Xenopus Ca2+-ligated calmodulin. This protein is comprised of two domains connected by two rigid helices joined by a flexible segment. It is possible to uniquely determine all "extended model-free" parameters without any a priori assumptions regarding their magnitudes by simultaneously least-squares fitting the relaxation data measured at two different magnetic fields. It is found that the two connecting helices (and consequently the domains) undergo slow motions relative to the conformation in which the two helices are parallel. The time scales and amplitudes of these "wobbling" motions are characterized by effective correlation times and squared-order parameters of approximately 3 ns and 0.7, respectively. These values are consistent with independent estimates indicating that this procedure provides a useful first-order description of complex internal motions in macromolecules despite neglecting the coupling of overall and interdomain motions.