Application of spherical harmonics for DEER data analysis in systems with a conformational distribution

Area of Science:

• Biophysics
• Chemical Physics
• Spectroscopy

Background:

• Double electron-electron resonance (DEER) and pulse electron paramagnetic resonance (EPR) are key for distance measurements between paramagnetic centers.
• Existing DEER theory is limited when relative orientations significantly affect data, often requiring model-based simulations.
• Orientation selection effects in DEER are not fully addressed by current analytical theories.

Purpose of the Study:

• To elaborate the theory of DEER, specifically addressing orientation selection effects in systems with moderate conformational disorder.
• To develop analytical and computational methods for extracting distance and orientation information from DEER data.
• To validate the developed theoretical framework and algorithms using experimental data.

Main Methods:

• Analytical treatment of DEER data using expansions into spherical harmonics to account for orientation distribution.
• Representation of DEER spectra with orientation selection as linear combinations of modified Pake pattern (MPP) components.
• Development of a model-free iterative processing algorithm based on Tikhonov regularization for disentangling distance and orientation information.

Main Results:

• Conformational disorder acts as a filter, suppressing higher-degree modified Pake pattern (MPP) components in DEER spectra.
• The developed theory enables model-based simulations with analytically defined orientation distributions.
• A novel iterative algorithm successfully disentangles distance and orientation information from multiple DEER datasets.
• Validation of both model-based and model-free approaches using a nitroxide biradical and a spin-labeled protein.

Conclusions:

• The developed spherical harmonics expansion theory provides crucial insights into DEER data structure under orientation selection effects.
• The new methods offer a robust pathway for analyzing complex systems where orientation distribution is significant.
• The validated approaches enhance the utility of DEER spectroscopy for structural studies of biomolecules and materials.