An Assessment of the Applicability of Multifrequency ESR to Study the Complex Dynamics of Biomolecules

Abstract

It is shown that the commonly used models for analyzing ESR spectra from nitroxide 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, which itself is relaxing on a longer time scale. This faster motion describes the internal dynamics, while the slower motion describes the global tumbling of the macromolecule. By using the SRLS model as the reference, it is shown (1) under what conditions the microscopic-order macroscopic-disorder (MOMD) 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 magnetic tensors, is valid. The frequency dependence of these models is studied. A key general property of high frequency ESR that emerges is that it reports 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 GHz), whereas, in general, the FIM model is a better approximation for low frequency (9 GHz) ESR spectra. However, in general, one does not find that the simpler model fits, at a single ESR frequency, to the more complete SRLS model, return correct motional and ordering parameters. The simultaneous fitting of both low and high frequency ESR spectra is thus required to remove such ambiguities and to return all the various dynamic, ordering, and geometric factors that characterize the complex dynamics. This approach is briefly related to recent ESR spectra from the spin-labeled protein, T4 lysozyme, and from spin-labeled DNA nucleosides. In order to better apply the slow-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 preferred orientation of the internal modes of motion is arbitrary.

An Improved Picture of Methyl Dynamics in Proteins from Slowly Relaxing Local Structure Analysis of 2H Spin Relaxation

“…The fundamentals of the stochastic coupled rotator slowly relaxing local structure (SRLS) theory 24,25 as applied to biomolecular dynamics 26 have been developed recently for NMR spin relaxation in proteins. [16][17][18][19][20][21][22][23] Two rotators, representing the global motion of the protein, R C , and the local motion of the probe (C-D bond in this case), R L , are treated.…”

“…L = 2, terms being preserved. 21,23,25,26 The coefficient (given in units of kB T) is a measure of the orientational ordering of the C-D bond with respect to the local director, C', whereas measures the asymmetry of the ordering around the director. Time correlation functions are calculated as: (6) Their Fourier-Laplace transforms yield the spectral densities j J MKK' (ω).…”

“…[16][17][18][19][20][21][22][23] This has been accomplished by applying to NMR spin relaxation in proteins 16 the Slowly Relaxing Local Structure (SRLS) approach of Freed and co-workers. [24][25][26] SRLS can be considered the generalization of MF, yielding the latter in asymptotic limits. 16,20,21,24 Unlike MF the SRLS model takes into account rigorously the dynamical coupling between the global motion of the protein and the local motion of the dynamic probe, brought into effect by a rhombic coupling potential.…”

“…It features explicitly local motional modes parallel and perpendicular to the methyl rotation axis. [16][17][18][19][20][21][22][23]25,26 and accounts rigorously for the tilt between a rhombic local ordering frame, M, and the magnetic frame, Q. The Euler angles Ω C'M , which relate the M frame to a local director frame, C' (e.g., the equilibrium C-CH 3 orientation), are governed by the coupling/ ordering potential.…”

“…For a M frame tilted relative to the Q frame the spectral density, J QQ (ω) (QQ denotes quadrupolar auto-correlated relaxation), comprises three generic spectral density functions, j K (ω), with K = 0, 1, 2 (refs. 16,25,26 ), by analogy with J(ω) for axial global diffusion of a rigid protein comprising three Lorentzian functions with K = 0, 1, 2. Yet, the MF spectral density consists of a single function which represents the K = 0 contribution.…”