FmRα analysis: Rapid and direct estimation of relaxation and kinetic parameters from dynamic nuclear polarization time courses

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

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 12 C lactate, cause an increase in the rate of exchange of the 13 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.

Kinetic Analysis of Hepatic Metabolism Using Hyperpolarized Dihydroxyacetone

Hyperpolarized carbon-13 magnetic resonance (HP-MR) is a new metabolic imaging method the does not use ionizing radiation. Due to the inherent chemical specificity of MR, not only tracer uptake but also downstream metabolism of the agent is detected in a straightforward manner. HP [2-¹³C] dihydroxyacetone (DHA) is a promising new agent that directly interrogates hepatic glucose metabolism. DHA has three metabolic fates in the liver: glucose production, glycerol production and potential inclusion into triglycerides, and oxidation in the tricarboxylic acid cycle. Each pathway is regulated by flux through multiple enzymes. Using Duhamel's formula, the kinetics of DHA metabolism is modeled, resulting in estimates of specific reaction rate constants. The multiple enzymatic steps that control DHA metabolism make more simplified methods for extracting kinetic data less than satisfactory. The described modeling paradigm effectively identifies changes in metabolism between gluconeogenic and glycogenolytic models of hepatic function.

Glyoxalase activity in human erythrocytes and mouse lymphoma, liver and brain probed with hyperpolarized 13C-methylglyoxal

Methylglyoxal is a faulty metabolite. It is a ubiquitous by-product of glucose and amino acid metabolism that spontaneously reacts with proximal amino groups in proteins and nucleic acids, leading to impairment of their function. The glyoxalase pathway evolved early in phylogeny to bring about rapid catabolism of methylglyoxal, and an understanding of the role of methylglyoxal and the glyoxalases in many diseases is beginning to emerge. Metabolic processing of methylglyoxal is very rapid in vivo and thus notoriously difficult to detect and quantify. Here we show that 13C nuclei in labeled methylglyoxal can be hyperpolarized using dynamic nuclear polarization, providing 13C nuclear magnetic resonance signal enhancements in the solution state close to 5,000-fold. We demonstrate the applications of this probe of metabolism for kinetic characterization of the glyoxalase system in isolated cells as well as mouse brain, liver and lymphoma in vivo.

Sub-minute kinetics of human red cell fumarase: 1 H spin-echo NMR spectroscopy and 13 C rapid-dissolution dynamic nuclear polarization

Fumarate is an important probe of metabolism in hyperpolarized magnetic resonance imaging and spectroscopy. It is used to detect the release of fumarase in cancer tissues, which is associated with necrosis and drug treatment. Nevertheless, there are limited reports describing the detailed kinetic studies of this enzyme in various cells and tissues. Thus, we aimed to evaluate the sub-minute kinetics of human red blood cell fumarase using nuclear magnetic resonance (NMR) spectroscopy, and to provide a quantitative description of the enzyme that is relevant to the use of fumarate as a probe of cell rupture. The fumarase reaction was studied using time courses of 1 H spin-echo and 13 C-NMR spectra. 1 H-NMR experiments showed that the fumarase reaction in hemolysates is sufficiently rapid to make its kinetics amenable to study in a period of approximately 3 min, a timescale characteristic of hyperpolarized 13 C-NMR spectroscopy. The rapid-dissolution dynamic nuclear polarization (RD-DNP) technique was used to hyperpolarize [1,4-13 C]fumarate, which was injected into concentrated hemolysates. The kinetic data were analyzed using recently developed FmRα analysis and modeling of the enzymatic reaction using Michaelis-Menten equations. In RD-DNP experiments, the decline in the 13 C-NMR signal from fumarate, and the concurrent rise and fall of that from malate, were captured with high spectral resolution and signal-to-noise ratio, which allowed the robust quantification of fumarase kinetics. The kinetic parameters obtained indicate the potential contribution of hemolysis to the overall rate of the fumarase reaction when 13 C-NMR RD-DNP is used to detect necrosis in animal models of implanted tumors. The analytical procedures developed will be applicable to studies of other rapid enzymatic reactions using conventional and hyperpolarized substrate NMR spectroscopy.

A comparison of quantitative methods for clinical imaging with hyperpolarized (13)C-pyruvate

Dissolution dynamic nuclear polarization (DNP) enables the metabolism of hyperpolarized (13)C-labelled molecules, such as the conversion of [1-(13)C]pyruvate to [1-(13)C]lactate, to be dynamically and non-invasively imaged in tissue. Imaging of this exchange reaction in animal models has been shown to detect early treatment response and correlate with tumour grade. The first human DNP study has recently been completed, and, for widespread clinical translation, simple and reliable methods are necessary to accurately probe the reaction in patients. However, there is currently no consensus on the most appropriate method to quantify this exchange reaction. In this study, an in vitro system was used to compare several kinetic models, as well as simple model-free methods. Experiments were performed using a clinical hyperpolarizer, a human 3 T MR system, and spectroscopic imaging sequences. The quantitative methods were compared in vivo by using subcutaneous breast tumours in rats to examine the effect of pyruvate inflow. The two-way kinetic model was the most accurate method for characterizing the exchange reaction in vitro, and the incorporation of a Heaviside step inflow profile was best able to describe the in vivo data. The lactate time-to-peak and the lactate-to-pyruvate area under the curve ratio were simple model-free approaches that accurately represented the full reaction, with the time-to-peak method performing indistinguishably from the best kinetic model. Finally, extracting data from a single pixel was a robust and reliable surrogate of the whole region of interest. This work has identified appropriate quantitative methods for future work in the analysis of human hyperpolarized (13)C data.