Mathematical Modeling and Data Analysis of NMR Experiments using Hyperpolarized (13)C Metabolites

Schulte R, Laustsen C. Comprehensive Literature Review of Hyperpolarized Carbon-13 MRI: The Road to Clinical Application

This review provides a comprehensive assessment of the development of hyperpolarized (HP) carbon-13 metabolic MRI from the early days to the present with a focus on clinical applications. The status and upcoming challenges of translating HP carbon-13 into clinical application are reviewed, along with the complexity, technical advancements, and future directions. The road to clinical application is discussed regarding clinical needs and technological advancements, highlighting the most recent successes of metabolic imaging with hyperpolarized carbon-13 MRI. Given the current state of hyperpolarized carbon-13 MRI, the conclusion of this review is that the workflow for hyperpolarized carbon-13 MRI is the limiting factor.

Catalytic cycle of carbohydrate dehydration by Lewis acids: structures and rates from synergism of conventional and DNP NMR

Structures and rates in the catalytic cycle of carbohydrate dehydration by Lewis acidic salt are determined through the systematic use of complementary NMR approaches.

Rapid zero-trans kinetics of Cs+ exchange in human erythrocytes quantified by dissolution hyperpolarized 133Cs+ NMR spectroscopy

Transmembrane flux of Cs⁺ (a K⁺ congener) was measured in human red blood cells (RBCs; erythrocytes) on the 10-s time scale. This is the first report on dissolution dynamic nuclear polarization (dDNP) nuclear magnetic resonance (NMR) spectroscopy with this nuclide in mammalian cells. Four technical developments regularized sample delivery and led to high quality NMR spectra. Cation-free media with the Piezo1 (mechanosensitive cation channel) activator yoda1 maximized the extent of membrane transport. First-order rate constants describing the fluxes were estimated using a combination of statistical methods in Mathematica, including the Markov chain Monte Carlo (MCMC) algorithm. Fluxes were in the range 4-70 μmol Cs⁺ (L RBC)^-1 s^-1; these are smaller than for urea, but comparable to glucose. Methodology and analytical procedures developed will be applicable to transmembrane cation transport studies in the presence of additional Piezo1 effectors, to other cellular systems, and potentially in vivo.

Combined In-Cell NMR and Simulation Approach to Probe Redox-Dependent Pathway Control

Dynamic response of intracellular reaction cascades to changing environments is a hallmark of living systems. As metabolism is complex, mechanistic models have gained popularity for describing the dynamic response of cellular metabolism and for identifying target genes for engineering. At the same time, the detailed tracking of transient metabolism in living cells on the subminute time scale has become amenable using dynamic nuclear polarization-enhanced ¹³C NMR. Here, we suggest an approach combining in-cell NMR spectroscopy with perturbation experiments and modeling to obtain evidence that the bottlenecks of yeast glycolysis depend on intracellular redox state. In pre-steady-state glycolysis, pathway bottlenecks shift from downstream to upstream reactions within a few seconds, consistent with a rapid decline in the NAD⁺/NADH ratio. Simulations using mechanistic models reproduce the experimentally observed response and help identify unforeseen biochemical events. Remaining inaccuracies in the computational models can be identified experimentally. The combined use of rapid injection NMR spectroscopy and in silico simulations provides a promising method for characterizing cellular reactions with increasing mechanistic detail.

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.

Influence of parameter accuracy on pharmacokinetic analysis of hyperpolarized pyruvate

PURPOSE

To explore the effects of noise and error on kinetic analyses of tumor metabolism using hyperpolarized [1-¹³ C] pyruvate.

METHODS

Numerical simulations were performed to systematically investigate the effects of noise, the number of unknowns, and error in kinetic parameter estimates on kinetic analysis of the apparent rate of chemical conversion from hyperpolarized pyruvate to lactate (k_PL ). A pharmacokinetic model with two physical and two chemical pools of hyperpolarized spins was used to generate and analyze the synthetic data.

RESULTS

The reproducibility of k_PL estimates worsened quickly when peak signal-to-noise ratio for hyperpolarized pyruvate was below approximately 20. The accuracy of k_PL estimates was most sensitive to errors in high excitation angles, the vascular blood volume fraction (v_b ), and the rate of pyruvate extravasation (k_ve ), and was least sensitive to errors in the T₁ of pyruvate. When v_b and/or k_ve were fit as additional unknowns, the accuracy of k_PL estimates suffered, and when the vascular input function of pyruvate was also fit, the reproducibility of k_PL estimates worsened.

CONCLUSIONS

The accuracy and precision of k_PL estimates improve substantially for peak signal-to-noise ratio above approximately 20. Accurate estimates of perfusion parameters (combinations of v_b , k_ve , and the pyruvate vascular input function) and transmit calibration at high excitation angles have the greatest effect on the accuracy of kinetic analyses. Magn Reson Med 79:3239-3248, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

NMR magnetization-transfer analysis of rapid membrane transport in human erythrocytes

Nuclear magnetic resonance (NMR) magnetization-transfer (MT) experiments provide a convenient tool for studying rapid sub-second membrane-transport processes in situ in metabolically active cells. These experiments are used with membrane-permeable substances when separate (resolved) NMR signals are observed from their populations inside and outside the cells. Here, we provide a description of the theory and practice of the most common NMR MT experiments that have been used to study membrane-transport processes in human erythrocytes (red blood cells; RBCs). The procedures, involved in the analysis of the experimental data for defining mechanisms of transport, and for estimating values of kinetic parameters in the corresponding mathematical models, are given special attention.

A novel perfused Bloch-McConnell simulator for analyzing the accuracy of dynamic hyperpolarized MRS

PURPOSE

Magnetic resonance spectroscopy of hyperpolarized agents allows real-time detection of metabolism in vivo. However, the nonrenewable nature of these signals necessitates data acquisitions that differ significantly from conventional magnetic resonance imaging. Signal evolution is permanently altered by the data acquisition scheme, potentially leading to sequence parameter-dependent bias in quantification. The authors have developed a novel simulation environment to characterize the effects of sequence parameters on magnetic resonance spectroscopy-based chemical exchange measurements using hyperpolarized pyruvate.

METHODS

Conventional Bloch-McConnell equations were coupled with a pharmacokinetic model for perfusion to allow realistic simulation of in vivo dynamic hyperpolarized signal evolution. In this study, simulations were conducted to explore effects of excitation angle and repetition time on the observed signal and subsequent parametric analysis. Both high and low apparent exchange rates were modeled under assumption of both perfused and closed systems. Bias due to sampling strategy bias was subsequently tested in vivo.

RESULTS

Simulation of dynamic magnetic resonance spectroscopy studies using hyperpolarized pyruvate demonstrated that for closed systems, accurate measurement of the apparent exchange rate was possible over a wide range of sequence parameters. This was true for both high and low apparent exchange rates, although a low exchange rate was associated with larger errors when excitation angles were high. When effects of perfusion were included to account for pyruvate delivery, a more restricted range of settings led to accurate quantification of exchange rates. Perfusion alleviated some of the errors seen at high excitation angles for low exchange rates. Residuals from parametric analysis did not generally correlate with fit accuracy, implying that the quality of the analysis model was not a major driver of error. Animal studies acquired with sequence parameters that are predicted to impart bias showed a significant under estimation of exchange rates (P < 0.035) compared to parameter combinations that are not expected to bias measurements.

CONCLUSIONS

The authors' results suggest that great care must be taken when measuring dynamic processes by magnetic resonance spectroscopy of hyperpolarized substrates. When comparing apparent exchange rates, choice of sequence parameters will affect the results. Bias introduced by parameters of more advanced acquisition and reconstruction schemes will likely increase compared to the relatively simple dynamic spectroscopy methods tested herein. The modified Bloch-McConnell equations the authors describe will be crucial tools for characterizing and optimizing the performance of these more advanced techniques.

The role of the glassy dynamics and thermal mixing in the dynamic nuclear polarization and relaxation mechanisms of pyruvic acid

The temperature dependence of (1)H and (13)C nuclear spin-lattice relaxation rate 1/T1 has been studied in the 1.6-4.2 K temperature range in pure pyruvic acid and in pyruvic acid containing trityl radicals at a concentration of 15 mM. The temperature dependence of 1/T1 is found to follow a quadratic power law for both nuclei in the two samples. Remarkably the same temperature dependence is displayed also by the electron spin-lattice relaxation rate 1/T1e in the sample containing radicals. These results are explained by considering the effect of the structural dynamics on the relaxation rates in pyruvic acid. Dynamic nuclear polarization experiments show that below 4 K the (13)C build up rate scales with 1/T1e, in analogy to (13)C 1/T1 and consistently with a thermal mixing scenario where all the electrons are collectively involved in the dynamic nuclear polarization process and the nuclear spin reservoir is in good thermal contact with the electron spin system.

Hyperpolarized NMR probes for biological assays

During the last decade, the development of nuclear spin polarization enhanced (hyperpolarized) molecular probes has opened up new opportunities for studying the inner workings of living cells in real time. The hyperpolarized probes are produced ex situ, introduced into biological systems and detected with high sensitivity and contrast against background signals using high resolution NMR spectroscopy. A variety of natural, derivatized and designed hyperpolarized probes has emerged for diverse biological studies including assays of intracellular reaction progression, pathway kinetics, probe uptake and export, pH, redox state, reactive oxygen species, ion concentrations, drug efficacy or oncogenic signaling. These probes are readily used directly under natural conditions in biofluids and are often directly developed and optimized for cellular assays, thus leaving little doubt about their specificity and utility under biologically relevant conditions. Hyperpolarized molecular probes for biological NMR spectroscopy enable the unbiased detection of complex processes by virtue of the high spectral resolution, structural specificity and quantifiability of NMR signals. Here, we provide a survey of strategies used for the selection, design and use of hyperpolarized NMR probes in biological assays, and describe current limitations and developments.

Transmembrane exchange of hyperpolarized 13C-urea in human erythrocytes: subminute timescale kinetic analysis

The rate of exchange of urea across the membranes of human erythrocytes (red blood cells) was quantified on the 1-s to 2-min timescale. (13)C-urea was hyperpolarized and subjected to rapid dissolution and the previously reported (partial) resolution of (13)C NMR resonances from the molecules inside and outside red blood cells in suspensions was observed. This enabled a stopped-flow type of experiment to measure the (initially) zero-trans transport of urea with sequential single-pulse (13)C NMR spectra, every second for up to ~2 min. Data were analyzed using Bayesian reasoning and a Markov chain Monte Carlo method with a set of simultaneous nonlinear differential equations that described nuclear magnetic relaxation combined with transmembrane exchange. Our results contribute to quantitative understanding of urea-exchange kinetics in the whole body; and the methodological approach is likely to be applicable to other cellular systems and tissues in vivo.