Analytical solution to the Lipari-Szabo model based on the reduced spectral density approximation offers a novel protocol for extracting motional parameters.

An analytical solution to the Lipari-Szabo model is derived for isotropic overall tumbling. The parameters of the original Lipari-Szabo model, the order parameter S2 and the effective internal correlation time tau(e), are calculated from two values of the spectral density function. If additionally the spectral density value J(0) is known, the exchange contribution R(ex) term can also be determined. The overall tumbling time tau(c) must be determined in advance, for example, from T1/T2 ratios. The required spectral density values are obtained by reduced spectral density mapping from T1, T2, and NOE measurements. Our computer simulations show that the reduced spectral density mapping is a very good approximation in almost all cases in which the Lipari-Szabo model is applicable. The robustness of the analytical formula to experimental errors is also investigated by extensive computer simulations and is found to be similar to that of the fitting procedures. The derived formulas were applied to the experimental 15N relaxation data of ubiquitin. Our results agree well with the published parameter values of S2 and tau(e), which were obtained from standard fitting procedures. The analytical approach to extract parameters of molecular motions may be more robust than standard analyses and provides a safeguard against spurious fitting results, especially for determining the exchange contribution R(ex). Copyright 2001 Academic Press.