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

Abstract

We describe a new model-free approach to solve the inverse problem in pulsed double electron-electron resonance (PELDOR, also known as DEER) spectroscopy and obtain the distance distribution function between two radicals from time-domain PELDOR data. The approach is based on analytical solutions of the Fredholm integral equations of the first kind using integral Mellin transforms to provide the distance distribution function directly. The approach appears to confine the noise in the computed distance distribution to short distances and does not introduce systematic distortions. Thus, the proposed analysis method can be a useful supplement to current methods to determine complicated distance distributions.

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

“…During PELDOR data processing, to obtain the distance distribution function P ( r ) between two spin labels in the DNA molecule, three approaches were employed: the conventional Tikhonov regularization approach (DeerAnalysis2013) ( 38 ), and two novel methods: multi-Gaussian regularization ( 39 ) and Mellin transformation ( 40 ).…”

Deep neural network processing of DEER data

“…In some site-directed spin labeling applications, an experimental estimate of the background can be obtained by measuring singly labeled constructs ( 15 ). Significant progress was also recently made with Mellin transform techniques ( 45 ) that are likely to improve further once the non-negativity constraint is introduced.…”

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

“…An analytical inverse solution of eqn (1) and (2) has been found that uses the Mellin Transform. 11,18,19 Using this solution, f (r) is calculated from the experimentally measured dipolar trace. For convenience, we will refer to this Mellin Transform analysis as MeTA.…”

“…Many approaches have been described to extract the distance distribution. [3][4][5][6][7][8][9][10][11][12][13][14] But no implementation is recognized as clearly superior; although the Tikhonov regularization method in DeerAnalysis 5 is a convenient benchmark for comparisons.…”

“…However, there is a Mellin Transform-based approach 11 to PDS data analysis that implements the regularization somewhat differently. It tries to make the experimental dipolar trace 'reasonable' according to eqn (1) in a way that affects only the noise s(r), independent of P(r) of V(T).…”