Analytical solution of the PELDOR inverse problem using the integral Mellin transform

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.

Non-uniform sampling in pulse dipolar spectroscopy by EPR: the redistribution of noise and the optimization of data acquisition

Pulse dipolar spectroscopy (PDS) in Electron Paramagnetic Resonance (EPR) is the method of choice for determining the distance distribution function for mono-, bi- or multi- spin-labeled macromolecules and nanostructures. PDS acquisition schemes conventionally use uniform sampling of the dipolar trace, but non-uniform sampling (NUS) schemes can decrease the total measurement time or increase the accuracy of the resulting distance distributions. NUS requires optimization of the data acquisition scheme, as well as changes in data processing algorithms to accommodate the non-uniformly sampled data. We investigate in silico the applicability of the NUS approach in PDS, considering its effect on random, truncation and sampling noise in the experimental data. Each type of noise in the time-domain data propagates differently and non-uniformly into the distance spectrum as errors in the distance distribution. NUS schemes seem to be a valid approach for increasing sensitivity and/or throughput in PDS by decreasing and redistributing noise in the distance spectrum so that it has less impact on the distance spectrum.

DeerLab: a comprehensive software package for analyzing dipolar electron paramagnetic resonance spectroscopy data

Dipolar EPR spectroscopy (DEER and other techniques) enables the structural characterization of macromolecular and biological systems by measurement of distance distributions between unpaired electrons on a nanometer scale. The inference of these distributions from the measured signals is challenging due to the ill-posed nature of the inverse problem. Existing analysis tools are scattered over several applications with specialized graphical user interfaces. This renders comparison, reproducibility, and method development difficult. To remedy this situation, we present DeerLab, an open-source software package for analyzing dipolar EPR data that is modular and implements a wide range of methods. We show that DeerLab can perform one-step analysis based on separable non-linear least squares, fit dipolar multi-pathway models to multi-pulse DEER data, run global analysis with non-parametric distributions, and use a bootstrapping approach to fully quantify the uncertainty in the analysis.

Bayesian Probabilistic Analysis of DEER Spectroscopy Data Using Parametric Distance Distribution Models

Double electron-electron resonance (DEER) spectroscopy measures distance distributions between spin labels in proteins, yielding important structural and energetic information about conformational landscapes. Analysis of an experimental DEER signal in terms of a distance distribution is a nontrivial task due to the ill-posed nature of the underlying mathematical inversion problem. This work introduces a Bayesian probabilistic inference approach to analyze DEER data, using a multi-Gauss mixture model for the distance distribution. The method uses Markov chain Monte Carlo (MCMC) sampling to determine a posterior probability distribution over model parameter space. This distribution contains all the information available from the data, including a full quantification of the uncertainty about the parameters. The corresponding uncertainty about the distance distribution is captured via an ensemble of posterior predictive distributions. Several synthetic examples illustrate the method. An experimental example shows the importance of model checking and comparison using residual analysis and Bayes factors. Overall, the Bayesian approach allows for more robust inference about protein conformations from DEER spectroscopy.

Substrate specificity of human apurinic/apyrimidinic endonuclease APE1 in the nucleotide incision repair pathway

Human apurinic/apyrimidinic (AP) endonuclease APE1 catalyses the hydrolysis of phosphodiester bonds on the 5′ side of an AP-site (in the base excision repair pathway) and of some damaged nucleotides (in the nucleotide incision repair pathway). The range of substrate specificity includes structurally unrelated damaged nucleotides. Here, to examine the mechanism of broad substrate specificity of APE1, we performed pulsed electron–electron double resonance (PELDOR) spectroscopy and pre-steady-state kinetic analysis with Förster resonance energy transfer (FRET) detection of DNA conformational changes during DNA binding and lesion recognition. Equilibrium PELDOR and kinetic FRET data revealed that DNA binding by APE1 leads to noticeable damage-dependent bending of a DNA duplex. Molecular dynamics simulations showed that the damaged nucleotide is everted from the DNA helix and placed into the enzyme’s binding pocket, which is formed by Asn-174, Asn-212, Asn-229, Ala-230, Phe-266 and Trp-280. Nevertheless, no damage-specific contacts were detected between these amino acid residues in the active site of the enzyme and model damaged substrates containing 1,N6-ethenoadenosine, α-adenosine, 5,6-dihydrouridine or F-site. These data suggest that the substrate specificity of APE1 is controlled by the ability of a damaged nucleotide to flip out from the DNA duplex in response to an enzyme-induced DNA distortion.

Deep neural network processing of DEER data

The established model-free methods for the processing of two-electron dipolar spectroscopy data [DEER (double electron-electron resonance), PELDOR (pulsed electron double resonance), DQ-EPR (double-quantum electron paramagnetic resonance), RIDME (relaxation-induced dipolar modulation enhancement), etc.] use regularized fitting. In this communication, we describe an attempt to process DEER data using artificial neural networks trained on large databases of simulated data. Accuracy and reliability of neural network outputs from real experimental data were found to be unexpectedly high. The networks are also able to reject exchange interactions and to return a measure of uncertainty in the resulting distance distributions. This paper describes the design of the training databases, discusses the training process, and rationalizes the observed performance. Neural networks produced in this work are incorporated as options into Spinach and DeerAnalysis packages.