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Biochemistry. 2018 Aug 7;57(31):4753-4763. doi: 10.1021/acs.biochem.8b00370. Epub 2018 Jul 30.

General Expressions for Carr-Purcell-Meiboom-Gill Relaxation Dispersion for N-Site Chemical Exchange.

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Department of Biochemistry and Molecular Biophysics , Columbia University , 630 West 168th Street , New York , New York 10032 , United States.
Department of Molecular Genetics, Biochemistry and Microbiology , University of Cincinnati , Cincinnati , Ohio 45267 , United States.


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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