Modeling excluded volume effects for the faithful description of the background signal in double electron-electron resonance

We discuss excluded volume effects on the background signal of double electron-electron resonance (DEER) experiments. Assuming spherically symmetric pervaded volumes, an analytical expression of the background signal is derived based on the shell-factorization approach. The effects of crowding and off-center label positions are discussed. Crowding is taken into account using the Percus-Yevick approximation for the radial distribution function of the particle centers. In addition, a versatile approach relating the pair-correlation function of the particle centers with those of off-center labels is introduced. Limiting expressions applying to short and long dipolar evolution times are derived. Furthermore, we show under which conditions the background with significant excluded volume effects resembles that originating from a fractal dimensionality ranging from 3 to 6. DEER time domain data of spin-probed samples of human serum albumin (HSA) are shown to be strongly affected by excluded-volume effects. The excluded volume is determined from the simultaneous analysis of spectra recorded at various protein concentrations but a constant probe-to-protein ratio. The spin-probes 5-DOXYL-stearic acid (5-DSA) and 16-DOXYL-stearic acid (16-DSA) are used, which, when taken up by HSA, give rise to broad and well-defined distance distributions, respectively. We compare different, model-free approaches of analyzing these data. The most promising results are obtained by the concurrent Tikhonov regularization of all spectra when a common background model is simultaneously adjusted such that the a posteriori probability is maximized. For the samples of 16-DSA in HSA, this is the only approach that allows suppressing a background artifact. We suggest that the delineated simultaneous analysis procedure can be generally applied to reduce ambiguities related to the ill-posed extraction of distance distributions from DEER spectra. This approach is particularly valuable for dipolar signals resulting from broad distance distributions, which as a consequence, are devoid of explicit dipolar oscillations.