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. We describe an approach to formulating the kinetic masterequations of the time evolution of NMR signals in reacting (bio)chemicalsystems. 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 reactionsmediated by enzymes and membrane transport proteins. We extend the workgiven in a recent presentation on this topic (Kuchel andShishmarev, 2020) to now include enzymes with two or more substrates andvarious enzyme reaction mechanisms as classified by Cleland, with particularreference to non-first-order processes. Using this approach, we can address some pressing questions in the field from a theoretical standpoint. Forexample, why does binding of a hyperpolarized substrate to an enzyme not causean appreciable loss of the signal from the substrate or product? Why doesthe concentration of an unlabelled pool of substrate, for example 12Clactate, cause an increase in the rate of exchange of the 13C-labelled pool? To what extent is the equilibrium position of the reaction perturbedduring administration of the substrate? The formalism gives a fullmechanistic understanding of the time courses derived and is of relevance toongoing clinical trials using these techniques.

magnetic resonance

Extended Bloch–McConnell equations for mechanistic analysis of hyperpolarized &amp;lt;sup&amp;gt;13&amp;lt;/sup&amp;gt;C magnetic resonance experiments on enzyme systems