A Bayesian statistical method for the detection and quantification of rotational diffusion anisotropy from NMR relaxation data

It has recently become more widely appreciated that the presence of rotatio nal diffusional anisotropy in proteins and other macromolecules can have a significant affect on the interpretation of NMR relaxation data in terms of molecular motion. In this paper, we show how commonly used NMR relaxation data (R-1, R-2, and NOE) obtained at two spectrometer frequencies can be an alyzed using a Bayesian statistical approach to reliably detect and quantif y the degree of rotational diffusion anisotropy. Our approach differs from previous methods in that it does not make assumptions concerning the intern al motions experienced by the residues which are used to quantify the diffu sion anisotropy, but rather averages the results over all internal motions consistent with the data. We demonstrate our method using synthetic data co rresponding to isotropic, axially symmetric anisotropic, and fully asymmetr ic anisotropic rotational diffusion, as well as experimental NMR data. We c ompare the Bayesian statistical approach with a widely used method for extr acting tumbling parameters using both synthetic and experimental data. Whil e it can be difficult to separate the effects of chemical exchange from rot ational anisotropy using this "standard" method, these effects are readily separated using Bayesian statistics. In addition, we find that the Bayesian statistical approach requires considerably less CPU time than an equivalen t standard analysis. (C) 2000 Academic Press.