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Updated: Feb 7, 2026

15N CPMG Relaxation Dispersion for the Investigation of Protein Conformational Dynamics on the µs-ms Timescale
Published on: April 19, 2021
General Expressions for Carr-Purcell-Meiboom-Gill Relaxation Dispersion for N-Site Chemical Exchange
Hans Koss1, Mark Rance2, Arthur G Palmer1
1Department of Biochemistry and Molecular Biophysics , Columbia University , 630 West 168th Street , New York , New York 10032 , United States.
Abstract:
The Carr-Purcell-Meiboom-Gill (CPMG) nuclear magnetic resonance experiment is widely used to characterize chemical exchange phenomena in biological macromolecules. Theoretical expressions for the nuclear spin relaxation rate constant for two-site chemical exchange during CPMG pulse trains valid for all time scales are well-known as are descriptions of N-site exchange in the fast limit. We have obtained theoretical expressions for N-site exchange outside of the fast limit by using approximations to an average Liouvillian describing the decay of magnetization during a CPMG pulse train. We obtain general expressions for CPMG experiments for any N-site scheme and all experimentally accessible time scales. For sufficiently slow chemical exchange, we obtain closed-form expressions for the relaxation rate constant and a general characteristic polynomial for arbitrary kinetic schemes. Furthermore, we highlight features that qualitatively characterize CPMG curves obtained for various N-site kinetic topologies, quantitatively characterize CPMG curves obtained from systems in various N-site exchange situations, and test distinguishability of kinetic models.
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