The wobbling-in-a-cone analysis of internal motion in macromolecules

The autocorrelation functions of second order generalized harmonics for the restricted librational motion of a spheroid were calculated using a wobbling-in-a-cone model. The model represents a motion intuitively abstracted from the multiple internal rotations of a side chain or the anisotropic libration of backbone segments in macromolecules. The exact correlation functions expressed by multiexponential decay were found well approximated by a single exponential decay where integrated areas of the exact and approximated functions were taken to be the same. The results were used to express the relaxation of nuclear spins caused by the fluctuation of the dipole–dipole interaction. The multiexponential nature of exact correlation functions was related to the concept of the relaxation spectrum.