Confidence Analysis of DEER Data and its Structural Interpretation with Ensemble-Biased Metadynamics

Given its ability to measure multicomponent distance distributions between electron-spin probes, Double Electron-Electron Resonance spectroscopy (DEER) has become a leading technique to assess the structural dynamics of biomolecules. However, methodologies to evaluate the statistical error of these distributions are not standard, often hampering a rigorous interpretation of the experimental results. Distance distributions are often determined from the experimental DEER data through a mathematical method known as Tikhonov regularization, but this approach makes rigorous error estimates difficult. Here, we build upon an alternative model-based approach in which the distance probability distribution is represented as a sum of Gaussian components and use propagation of errors to calculate an associated confidence band. Our approach considers all sources of uncertainty, including the experimental noise, the uncertainty in the fitted background signal, and the limited time-span of the data collection. The resulting confidence band reveals the most and least reliable features of the probability distribution, thereby informing the structural interpretation of DEER experiments. To facilitate this interpretation, we also generalize the molecular-simulation method known as Ensemble-Biased Metadynamics. This method, originally designed to generate maximum-entropy structural ensembles consistent with one or more probability distributions, now also accounts for the uncertainty in those target distributions, exactly as dictated by their confidence bands. After careful benchmarks, we demonstrate the proposed techniques using DEER results from spin-labeled T4 lysozyme.