A Bayesian approach to quantifying uncertainty from experimental noise in DEER spectroscopy.

Double Electron-Electron Resonance (DEER) spectroscopy is a solid-state pulse Electron Paramagnetic Resonance (EPR) experiment that measures distances between unpaired electrons, most commonly between protein-bound spin labels separated by 1.5-8nm. From the experimental data, a distance distribution P(r) is extracted using Tikhonov regularization. The disadvantage of this method is that it does not directly provide error bars for the resulting P(r), rendering correct interpretation difficult. Here we introduce a Bayesian statistical approach that quantifies uncertainty in P(r) arising from noise and numerical regularization. This method provides credible intervals (error bars) of P(r) at each r. This allows practitioners to answer whether or not small features are significant, whether or not apparent shoulders are significant, and whether or not two distance distributions are significantly different from each other. In addition, the method quantifies uncertainty in the regularization parameter.