Estimation of dynamic parameters from NMR relaxation data using the Lipari-Szabo model-free approach and Bayesian statistical methods.

In order to analyze NMR relaxation data in terms of parameters which describe internal motion, one must first obtain a description of the overall tumbling of the macromolecule in solution. Methods currently used to estimate these global parameters may not always provide reliable estimates of their values and uncertainties. In this paper, we present a general data analysis formalism based on products of Bayesian marginal probability densities which can be used to efficiently combine the information content from multiple experiments, such as R(1), R(2), and NOE data collected at multiple magnetic field strengths, or data from cross-correlation or rotating frame relaxation dispersion experiments. Our approach allows the estimation of global tumbling and internal dynamical parameters and their uncertainties without some of the assumptions which are made in the commonly-used methods for model-selection and global parameter estimation. Compared to an equivalent classical statistical approach, the Bayesian method not only is more computationally efficient, but also provides greater insight into the information content of the data. We demonstrate that this approach can be used to estimate both the isotropic rotational correlation time in the context of the original and "extended" Lipari-Szabo formalisms [Lipari & Szabo, J. Am. Chem. Soc. 1982, 104, 4546; Clore et al., J. Am. Chem. Soc. 1990, 112, 4989], as well as the rotational diffusion coefficients for axially symmetric anisotropic tumbling.