Site-based description of R_1ρ relaxation in local reference frames

Area of Science:

• Biophysics
• Chemical Kinetics
• Magnetic Resonance Spectroscopy

Background:

• Nuclear magnetic spin relaxation is crucial for understanding biological macromolecules.
• Chemical exchange processes significantly influence spin relaxation dynamics.
• Existing methods for analyzing chemical exchange in R1ρ relaxation dispersion, CEST, and DEST experiments have limitations.

Purpose of the Study:

• To reformulate expressions for magnetization evolution and R1ρ relaxation rate.
• To develop a theoretical approach for simplifying chemical exchange topologies.
• To provide accurate approximations for spin relaxation under radiofrequency fields.

Main Methods:

• Focusing on rotating frames of reference for magnetization components.
• Treating spin-locking field strength as a perturbation.
• Applying Homotopy Analysis and Laplace transform methods to Bloch-McConnell equations.

Main Results:

• An R1ρ expression invariant to kinetic scheme topology was derived.
• An approximate equation for spin-locked z-magnetization evolution was obtained.
• An effective simplification approach for 2- and N-site chemical exchange was developed.

Conclusions:

• The developed theoretical approach offers powerful insights into chemical and conformational kinetics.
• The new methods enhance the characterization of chemical exchange processes in biological systems.
• Accurate approximations for relaxation in the absence of exchange were achieved.