Confidence limits in pulse dipolar EPR spectroscopy: estimates for individual measurements

The distribution of inter-label distances obtained by electron paramagnetic resonance (EPR) pulse dipolar spectroscopies (PDS), such as DEER aka PELDOR, gives a valuable characterization of structure on the nanometer scale. The impact of random experimental noise on such experiments is examined for three independent methods for analysing PDS data: the model-free method with Tikhonov regularization, model-free with Mellin-transformation, and a model-based method. All three methods show negative bias for the mean distance and positive bias for the distribution width. Both biases grow with increasing noise levels. The estimated confidence bands and the uncertainties obtained from a single experimental measurement by the standard bootstrapping or χ²-surface scanning approaches are inconsistent and can exclude the true distance distribution. Yet, both approaches can provide quite valuable support for hypothesis testing in PDS studies.