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

Area of Science:

• Biophysics
• Spectroscopy
• Computational Chemistry

Background:

• Pulsed double electron-electron resonance (PELDOR), also known as DEER, is a powerful technique for measuring distances between electron spins in molecules.
• Extracting accurate distance distribution functions from PELDOR data can be challenging, especially for complex systems.
• Current methods often rely on models or can introduce distortions and noise into the results.

Purpose of the Study:

• To develop a novel model-free approach for solving the inverse problem in PELDOR spectroscopy.
• To directly obtain the distance distribution function between two radicals from time-domain PELDOR data.
• To provide a robust and accurate analysis method for complex distance distributions.

Main Methods:

• The study employs analytical solutions to Fredholm integral equations of the first kind.
• Integral Mellin transforms are utilized to directly compute the distance distribution function.
• The method is model-free, avoiding assumptions about the underlying distribution.

Main Results:

• The proposed approach successfully obtains the distance distribution function directly from time-domain PELDOR data.
• Noise in the computed distance distribution is effectively confined to shorter distances.
• The method does not introduce systematic distortions into the analysis.
• The technique demonstrates potential for analyzing complex distance distributions.

Conclusions:

• The new model-free method offers a direct and accurate way to analyze PELDOR data.
• This approach can serve as a valuable supplement to existing techniques for determining complex distance distributions.
• The findings contribute to advancing the capabilities of electron spin resonance spectroscopy analysis.