Beyond the decoupling approximation in the model free approach for the interpretation of NMR relaxation of macromolecules in solution.

The model free (MF) approach allows straightforward extraction of generalized order parameters and correlation times for internal and overall bond vector reorientational fluctuations from NMR spin relaxation measurements for macromolecules in solution. The drawback of this approach is the use of a decoupling approximation that neglects correlations between internal and overall molecular motions. These correlations are significant when fluctuation amplitudes are less than the size of the "cage" that restricts the bond vector. In this regime, motion of the bond vector is only indirectly affected by molecule fluctuations through the orienting potential for the local director axis. By separating the regimes of large and small amplitude molecular fluctuations, an expression for the spectral density function is derived that does not invoke the decoupling approximation, but that relies on the same macroscopic level of description as the original MF approach. The parameters of the spectral density function provide insight into the effects on the MF parameters that result from violation of the decoupling approximation.