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 (Kuchel and Shishmarev, 2020) to now include enzymes with two or more substrates and various enzyme reaction mechanisms as classified by Cleland, with particular reference to non-first-order processes. 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 C lactate, cause an increase in the rate of exchange of the C-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.
Highlights
Nuclear magnetic resonance (NMR) spectroscopy and imaging (MRI) are widely employed techniques with far-reaching applications in physics, chemistry, medicine and the life sciences
Recent work has shown that the sensitivity of NMR experiments can be improved by using non-equilibrium hyperpolarization techniques such as dissolution dynamic nuclear polarization to boost signal intensities by many orders of magnitude (ArdenkjaerLarsen et al, 2003)
For first-order reactions, the hyperpolarized magnetization evolves according to the Bloch–McConnell equations, while the concentrations given by the sum of the “hot” and “cold” pools evolve according to the conventional form of chemical reaction kinetics for a closed system
Summary
Nuclear magnetic resonance (NMR) spectroscopy and imaging (MRI) are widely employed techniques with far-reaching applications in physics, chemistry, medicine and the life sciences. Recent work has shown that the sensitivity of NMR experiments can be improved by using non-equilibrium hyperpolarization techniques such as dissolution dynamic nuclear polarization (dDNP) to boost signal intensities by many orders of magnitude (ArdenkjaerLarsen et al, 2003) Such techniques have led to new applications (Golman et al, 2003, 2006; Keshari and Wilson, 2014) and necessitated the development of acquisition strategies to exploit the hyperpolarized magnetization in a time-efficient manner (Yen et al, 2009) as well as new tools for signal processing and image reconstruction (Hu et al, 2010). These equations are grounded in the concept of conservation of mass of the species responsible for the hyperpolarized signal plus its non-hyperpolarized counterpart and the various products; this was recently highlighted (Kuchel and Shishmarev, 2020) where the MR-visible signal decays to produce an MR-invisible one
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