Model-Free Approach to the Interpretation of Nuclear Magnetic Resonance Relaxation in Macromolecules. 1. Theory and Range of Validity

Abstract

A new approach to the interpretation of nuclear magnetic resonance relaxation experiments on macromolecules in solution is presented. This paper deals with the theoretical foundations and establishes the range of validity of this approach, and the accompanying paper demonstrates how a wide variety of experimental relaxation data can be successfully analyzed by using this approach. For both isotropic and anisotropic overall motion, it is shown that the unique information on fast internal motions contained in relaxation experiments can be completely specified by two model-independent quantities: (1) a generalized order parameter, δ, which is a measure of the spatial restriction of the motion, and (2) an effective correlation time, τe, which is a measure of the rate of motion. A simple expression for the spectral density involving these two parameters is derived and is shown to be exact when the internal (but not overall) motions are in the extreme narrowing limit. The model-free approach (so called because δ2 and τe have model-independent significance) consists of using the above spectral density to least-squares fit relaxation data by treating δ 2 and τe as adjustable parameters. The range of validity of this approach is illustrated by analyzing error-free relaxation data generated by using sophisticated dynamical models. Empirical rules are presented that allow one to estimate the accuracy of δ2 and τe extracted by using the model-free approach by considering their numerical values, the resonance frequencies, and the parameters for the overall motion. For fast internal motions, it is unnecessary to use approaches based on complicated spectral densities derived within the framework of a model because all models that can give the correct value of δ2 work equally well. The unique dynamic information ($ and τe) can be easily extracted by using the model-free approach. Moreover, if one desires a physical picture of the motion, the numerical values of δ2 and τe can be readily interpreted within a physically reasonable model. © 1982, American Chemical Society. All rights reserved.