Using the Model Free Approach to Analyze NMR Relaxation Data in Cases of Anisotropic Molecular Diffusion

Abstract

The model free approach, parameterized for the limiting case of isotropic molecular diffusion, is most often used to derive motional dynamics information from NMR relaxation data. However, many, if not most, biomolecules are asymmetric in shape and diffuse anisotropically in solution. Here, model free parameters have been derived to analyze NMR relaxation data for molecules undergoing anisotropic rotational diffusion. A simple correlation function has been formulated wherein restricted internal bond rotations are described by two parameters: 〈x2 + y2〉 and 〈x2 − y2〉. In the molecular frame, x and y are projections of motional unit vector a onto the plane that is perpendicular to the average position of vector a. For isotropic overall tumbling, this correlation function is reduced to a single parameter, 〈x2 + y2〉, which is related to the well-known model free order parameter as S2 = 1−3 〈x2 + y2〉. The term 〈x2 − y2〉 becomes important and takes on a value for molecules tumbling anisotropically in solution. Various motional models are expressed in terms of 〈x2 + y2〉 and 〈x2 - y2〉, and the influence of rotational correlations, described by coefficients −1 < cij < 1, are considered. A simple protocol for using this new anisotropic motional model is provided, along with an example on a small α-helical peptide.