Molecular orientation studies by pulsed electron-electron double resonance experiments.

Pulsed electron-electron double resonance (PELDOR) has proven to be a valuable tool to measure the distribution of long range distances in noncrystalline macromolecules. These experiments commonly use nitroxide spin labels as paramagnetic markers that are covalently attached to the macromolecule at specific positions. Unless these spin labels are flexible in such a manner that they exhibit an almost random orientation, the PELDOR signals will-apart from the interspin distance-also depend on the orientation of the spin labels. This effect needs to be considered in the analysis of PELDOR signals and can, moreover, be used to obtain additional information on the structure of the molecule under investigation. In this work, we demonstrate that the PELDOR signal can be represented as a convolution of a kernel function containing the distance distribution function and an orientation intensity function. The following strategy is proposed to obtain both functions from the experimental data. In a first step, the distance distribution function is estimated by the Tikhonov regularization, using the average over all PELDOR time traces with different frequency offsets and neglecting angular correlations of the spin labels. Second, the convolution relation is employed to determine the orientation intensity function, using again the Tikhonov regularization. Adopting small nitroxide biradical molecules as simple examples, it is shown that the approach works well and is internally consistent. Furthermore, independent molecular dynamics simulations are performed and used to calculate PELDOR signals, distance distributions, and orientational intensity functions. The calculated and experimental results are found to be in excellent overall agreement.