An assessment of the applicability of multifrequency ESR to study the complex dynamics of biomolecules

It is shown that the commonly used models for analyzing ESR spectra from ni troxide spin-labeled proteins or DNA systems are special cases of the more general slowly relaxing local structure (SRLS) model, wherein the nitroxide spin probe is taken as reorienting in a restricted local environment, whic h itself is relaxing on a longer time scale. This faster motion describes t he internal dynamics, while the slower motion describes the global tumbling of the macromolecule. By using the SRLS model as the reference, it is show n (1) under what conditions the microscopic-order macroscopic-disorder (MOM D) model, wherein the global tumbling of the macromolecule is in the rigid limit, is valid, and (2) when the fast internal motion (FIM) model, wherein the internal motion is so rapid as to lead to partial averaging of the mag netic tensors, is valid. The frequency dependence of these models is studie d. A key general property of high frequency ESR that emerges is that it rep orts on a faster motional time scale, whereas low frequency ESR reports on a slower motional time scale. It is shown that, in general, the MOMD model is a better approximation for ESR spectra obtained at high frequency (250 G Hz), whereas, in general, the FIM model is a better approximation for low f requency (9 GHz) ESR spectra. However, in general, one does not find that t he simpler model fits, at a single ESR frequency, to the more complete SRLS model, return correct motional and ordering parameters. The simultaneous f itting of both low and high frequency ESR spectra is thus required to remov e such ambiguities and to return all the various dynamic, ordering, and geo metric factors that characterize the complex dynamics. This approach is bri efly related to recent ESR spectra from the spin-labeled protein, T4 lysozy me, and from spin-labeled DNA nucleosides. In order to better apply the slo w-motional SRLS model to macromolecular dynamics, the Polimeno-Freed theory has been extended to the case where the global tumbling is anisotropic and where the angle between the principal axis of the global motion and the pr eferred orientation of the internal modes of motion is arbitrary.