Preprints
https://doi.org/10.5194/mr-2021-14
https://doi.org/10.5194/mr-2021-14

  16 Feb 2021

16 Feb 2021

Review status: this preprint is currently under review for the journal MR.

Extended Bloch-McConnell equations for mechanistic analysis of hyperpolarized 13C magnetic resonance experiments on enzyme systems

Thomas R. Eykyn1, Stuart J. Elliott2,a, and Philip W. Kuchel3 Thomas R. Eykyn et al.
  • 1School of Biomedical Engineering and Imaging Sciences, King’s College London, St Thomas’ Hospital, London SE1 7EH, United Kingdom
  • 2Centre de Résonance Magnétique Nucléaire à Très Hauts Champs - FRE 2034 Université de Lyon/CNRS/Université Claude Bernard Lyon 1/ENS de Lyon, 5 Rue de la Doua, 69100 Villeurbanne, France
  • 3School of Life and Environmental Sciences, University of Sydney, NSW 2006, Australia
  • acurrent address: Department of Chemistry, University of Liverpool, Liverpool L69 7ZD, United Kingdom

Abstract. We describe an approach to formulating the kinetic master equations of the time evolution of NMR signals in reacting (bio)chemical systems. Special focus is given to studies that employ signal enhancement (hyperpolarization) methods such as dissolution dynamic nuclear polarization (dDNP) and involving nuclear spin-bearing solutes that undergo reactions mediated by enzymes and membrane transport proteins. We extend the work given in a recent presentation on this topic to now include enzymes with two or more substrates and various enzyme reaction mechanisms as classified by Cleland. Using this approach, we can address some pressing questions in the field from a theoretical standpoint. For example, why does binding of a hyperpolarized substrate to an enzyme not cause an appreciable loss of the signal from the substrate or product? Why does the concentration of an unlabelled pool of substrate, for example 12C lactate, cause an increase in the rate of exchange of the 13C labelled pool? To what extent is the equilibrium position of the reaction perturbed during administration of the substrate? The formalism gives a full mechanistic understanding of the time courses derived and is of relevance to ongoing clinical trials using these techniques.

Thomas R. Eykyn et al.

Status: open (until 21 Mar 2021)

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Thomas R. Eykyn et al.

Thomas R. Eykyn et al.

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Short summary
An approach is described for formulating the kinetic master equations of the time evolution of hyperpolarized NMR signals in reacting (bio)chemical systems. We take a stepwise approach to formulate mathematical models of enzyme systems that agree with standard descriptions of (bio)chemical kinetics while remaining capable of describing the time evolution of magnetization described by the Bloch-McConnell equations.