Anisotropic rotational diffusion studied by passage saturation transfer electron paramagnetic resonance

Abstract

The stochastic Liouville equation for the spin density matrix is modified to consider the effects of Brownian anisotropic rotational diffusion upon electron paramagnetic resonance (EPR) and saturation transfer electron paramagnetic resonance (ST–EPR) spectra. Spectral shapes and the ST–EPR parameters L″/L, C′/C, and H″/H defined by Thomas, Dalton, and Hyde at X-band microwave frequencies [J. Chem. Phys. 65, 3006 (1976)] are examined and discussed in terms of the rotational times τ∥ and τ⊥ and in terms of other defined correlation times for systems characterized by magnetic tensors of axial symmetry and for systems characterized by nonaxially symmetric magnetic tensors. For nearly axially symmetric magnetic tensors, such as nitroxide spin labels studied employing 1–3 GHz microwaves, ST–EPR spectra for systems undergoing anisotropic rotational diffusion are virtually indistinguishable from spectra for systems characterized by isotropic diffusion. For nonaxially symmetric magnetic tensors, such as nitroxide spin labels studied employing 8–35 GHz microwaves, the high field region of the ST–EPR spectra, and hence the H″/H parameter, will be virtually indistinguishable from spectra, and parameter values, obtained for isotropic diffusion. On the other hand, the central spectral region at x-band microwave frequencies, and hence the C′/C parameter, is sensitive to the anisotropic diffusion model provided that a unique and static relationship exists between the magnetic and diffusion tensors. Random labeling or motion of the spin label relative to the biomolecule whose hydrodynamic properties are to be investigated will destroy spectral sensitivity to anisotropic motion. The sensitivity to anisotropic motion is enhanced in proceeding to 35 GHz with the increased sensitivity evident in the low field half of the EPR and ST–EPR spectra. The L″/L parameter is thus a meaningful indicator of anisotropic motion when compared with H″/H parameter analysis. However, consideration of spectral shapes suggests that the C′/C parameter definition is not meaningfully extended from 9.5 to 35 GHz. Alternative definitions of the L″/L and C′/C parameters are proposed for those microwave frequencies for which the electron Zeeman anisotropy is comparable to or greater than the electron–nitrogen nuclear hyperfine anisotropy.