Simulation of saturation transfer electron paramagnetic resonance spectra for rotational motion with restricted angular amplitude

We have simulated both conventional (V1) and saturation transfer (V'2) electron paramagnetic resonance spectra for the case of Brownian rotational diffusion restricted in angular amplitude. Numerical solutions of the diffusion-coupled Bloch equations were obtained for an axially symmetric 14N nitroxide spin label with its principal axis rotating within a Gaussian angular distribution of full width delta theta at half maximum. Spectra were first calculated for a macroscopically oriented system with cylindrical symmetry (e.g., a bundle of muscle fibers or a stack of membrane bilayers), with the Gaussian angular distribution centered at theta 0 with respect to the magnetic field. These spectra were then summed over theta 0 to obtain the spectrum of a randomly oriented sample (e.g., a dispersion of myofibrils or membrane vesicles). The angular amplitude delta theta was varied from 0 degrees, corresponding to isotropic motion (order parameter = 0). For each value of delta theta, the rotational correlation time, tau r, was varied from 10(-7) to 10(-2) s, spanning the range from maximal to minimal saturation transfer. We provide plots that illustrate the dependence of spectral parameters on delta theta and tau r. For an oriented system, the effects of changing delta theta and tau r are easily distinguishable, and both parameters can be determined unambiguously by comparing simulated and experimental spectra. For a macroscopically disordered system, the simulated spectra are still quite sensitive to delta theta, but a decrease in tau r produces changes similar to those from an increase in delta theta. If delta theta can be determined independently, then the results of the present study can be used to determine tau r from experimental spectra. Similarly, if tau r is known, then delta theta can be determined.