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

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.

SUBMITTER: Koss H

PROVIDER: S-EPMC6315113 | biostudies-literature | 2018 Aug

REPOSITORIES: biostudies-literature

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

Koss Hans H Rance Mark M Palmer Arthur G AG

Biochemistry 20180730 31

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 ...[more]

PMID: 30040382

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Project description:To study microsecond processes by relaxation dispersion NMR spectroscopy, low power deposition and short pulses are crucial and encourage the development of experiments that employ (1)H Carr-Purcell-Meiboom-Gill (CPMG) pulse trains. Herein, a method is described for the comprehensive study of microsecond to millisecond time scale dynamics of methyl groups in proteins, exploiting their high abundance and favorable relaxation properties. In our approach, protein samples are produced using [(1)H, (13)C]-d-glucose in ?100% D(2)O, which yields CHD(2) methyl groups for alanine, valine, threonine, isoleucine, leucine, and methionine residues with high abundance, in an otherwise largely deuterated background. Methyl groups in such samples can be sequence-specifically assigned to near completion, using (13)C TOCSY NMR spectroscopy, as was recently demonstrated (Otten, R.; et al. J. Am. Chem. Soc. 2010, 132, 2952-2960). In this Article, NMR pulse schemes are presented to measure (1)H CPMG relaxation dispersion profiles for CHD(2) methyl groups, in a vein similar to that of backbone relaxation experiments. Because of the high deuteration level of methyl-bearing side chains, artifacts arising from proton scalar coupling during the CPMG pulse train are negligible, with the exception of Ile-?1 and Thr-?2 methyl groups, and a pulse scheme is described to remove the artifacts for those residues. Strong (13)C scalar coupling effects, observed for several leucine residues, are removed by alternative biochemical and NMR approaches. The methodology is applied to the transcriptional activator NtrC(r), for which an inactive/active state transition was previously measured and the motions in the microsecond time range were estimated through a combination of backbone (15)N CPMG dispersion NMR spectroscopy and a collection of experiments to determine the exchange-free component to the transverse relaxation rate. Exchange contributions to the (1)H line width were detected for 21 methyl groups, and these probes were found to collectively report on a local structural rearrangement around the phosphorylation site, with a rate constant of (15.5 ± 0.5) × 10(3) per second (i.e., ?(ex) = 64.7 ± 1.9 ?s). The affected methyl groups indicate that, already before phosphorylation, a substantial, transient rearrangement takes place between helices 3 and 4 and strands 4 and 5. This conformational equilibrium allows the protein to gain access to the active, signaling state in the absence of covalent modification through a shift in a pre-existing dynamic equilibrium. Moreover, the conformational switching maps exactly to the regions that differ between the solution NMR structures of the fully inactive and active states. These results demonstrate that a cost-effective and quantitative study of protein methyl group dynamics by (1)H CPMG relaxation dispersion NMR spectroscopy is possible and can be applied to study functional motions on the microsecond time scale that cannot be accessed by backbone (15)N relaxation dispersion NMR. The use of methyl groups as dynamics probes extends such applications also to larger proteins.

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

Publications

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

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