Bayesian Statistical Methods in the Analysis of DEER Data

Abstract

Double Electron-Electron Resonance (DEER), also known as Pulsed Electron Double Resonance (PELDOR), is an increasingly important pulsed Electron Paramagnetic Resonance (EPR) technique for long distance (20-80 A) measurements in biomacromolecules. Notably, DEER reports a distribution of distances, P(r), corresponding to protein conformational ensembles in frozen glassy solutions. Due to the ill-conditioned, inverse nature of DEER data analysis, numerical regularization is required to obtain P(r). Further, a robust method for quantifying uncertainty in DEER distance distributions does not currently exist, complicating interpretation. Here, we compare methods of regularization parameter selection and demonstrate Bayesian statistical methods to quantify uncertainty in DEER distance distributions arising from measurement noise. We generate corresponding Bayesian credible intervals for visualization and interpretation.