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An R1ρ expression for a spin in chemical exchange between two sites with unequal transverse relaxation rates

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Abstract

An analytical expression is derived for the rotating frame relaxation rate, R 1ρ , of a spin exchanging between two sites with different transverse relaxation times. A number of limiting cases are examined, with the equation reducing to formulae derived previously under the assumption of equivalent relaxation rates at each site. The measurement of a pair off-resonance R 1ρ values, with the carrier displaced equally on either side of the observed correlation, forms the basis of one of the approaches for obtaining signs of chemical shift differences, Δω, of exchanging nuclei. The results presented here establish that this method is relatively insensitive to differential transverse relaxation rates between the exchaning states, greatly simplifying the calculation of optimal parameters in R 1ρ based experiments that are used for measurement of signs of Δω.

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Acknowledgments

A.J.B. acknowledges the Canadian Institutes of Health Research (CIHR) for a postdoctoral fellowship and the BBSRC and Merton College for David Phillips and Fitzjames fellowships respectively. This work was supported by grants from the CIHR and the Natural Sciences and Engineering Research Council of Canada. L.E.K. holds a Canada Research Chair in Biochemistry.

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  1. Andrew J. Baldwin

    Present address: Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford, OX1 3QZ, UK

Authors and Affiliations

  1. Departments of Molecular Genetics, Biochemistry and Chemistry, University of Toronto, Toronto, ON, M5S 1A8, Canada

    Andrew J. Baldwin & Lewis E. Kay

  2. Hospital for Sick Children, Program in Molecular Structure and Function, 555 University Avenue, Toronto, ON, M5G 1X8, Canada

    Lewis E. Kay

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  1. Andrew J. Baldwin
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  2. Lewis E. Kay
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Correspondence to Andrew J. Baldwin.

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Baldwin, A.J., Kay, L.E. An R1ρ expression for a spin in chemical exchange between two sites with unequal transverse relaxation rates. J Biomol NMR 55, 211–218 (2013). https://doi.org/10.1007/s10858-012-9694-6

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  • DOI: https://doi.org/10.1007/s10858-012-9694-6

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