Essential Tools of Linear Algebra for Calculating Nuclear Spin Dynamics of Chemically Exchanging Systems

In this work, we describe essential tools of linear algebra necessary for calculating the effect of chemical exchange on spin dynamics and polarization transfer in various nuclear magnetic resonance (NMR) experiments. We show how to construct Hamiltonian, relaxation, and chemical exchange superoperators in the Liouville space, as well as demonstrate corresponding code in Python. Examples of applying the code are given for problems involving chemical exchange between NH3 and NH4+ at zero and high magnetic field and polarization transfer from parahydrogen relevant in SABRE (signal amplification by reversible exchange) at low magnetic field (0-20 mT). The presented methodology finds utility for describing the effect of chemical exchange on NMR spectra and can be extended further by taking into account non-linearities in the master equation

13^{13}C and 15^{15}N benchtop NMR detection of metabolites via relayed hyperpolarization

Parahydrogen-based nuclear spin hyperpolarization allows various magnetic-resonance applications, and it is particularly attractive because of its technical simplicity, low cost, and ability to quickly (in seconds) produce large volumes of hyperpolarized material. Although many parahydrogen-based techniques have emerged, some of them remain unexplored due to the lack of careful optimization studies. In this work, we investigate and optimize a novel parahydrogen-induced polarization (PHIP) technique that relies on proton exchange referred to below as PHIP-relay. An INEPT (insensitive nuclei enhanced by polarization transfer) sequence is employed to transfer polarization from hyperpolarized protons to heteronuclei ($^{15}$N and $^{13}$C) and nuclear signals are detected using benchtop NMR spectrometers (1 T and 1.4 T, respectively). We demonstrate the applicability of the PHIP-relay technique for hyperpolarization of a wide range of biochemicals by examining such key metabolites as urea, ammonium, glucose, amino acid glycine, and a drug precursor benzamide. By optimizing chemical and NMR parameters of the PHIP-relay, we achieve a 17,100-fold enhancement of $^{15}$N signal of [$^{13}$C, $^{15}$N$_{2}$]-urea compared to the thermal signal measured at 1 T. We also show that repeated measurements with shorter exposure to parahydrogen provide a higher effective signal-to-noise ratio compared to longer parahydrogen bubbling

Zero-Field J-spectroscopy of Quadrupolar Nuclei

Zero- to ultralow-field (ZULF) nuclear magnetic resonance (NMR) is a version of NMR that allows studying molecules and their transformations in the regime dominated by intrinsic spin-spin interactions. While spin dynamics at zero magnetic field can be probed indirectly, J-spectra can also be measured at zero field by using non-inductive sensors, for example, optically-pumped magnetometers (OPMs). A J-spectrum can be detected when a molecule contains at least two different types of magnetic nuclei (i.e., nuclei with different gyromagnetic ratios) that are coupled via J-coupling. Up to date, no pure J-spectra of molecules featuring the coupling to quadrupolar nuclei were reported. Here we show that zero-field J-spectra can be collected from molecules containing quadrupolar nuclei with I = 1 and demonstrate this for solutions containing various isotopologues of ammonium cations. Lower ZULF NMR signals are observed for molecules containing larger numbers of deuterons compared to protons; this is attributed to less overall magnetization and not to the scalar relaxation of the second kind. We analyze the energy structure and allowed transitions for the studied molecular cations in detail using perturbation theory and demonstrate that in the studied systems, different lines in J-spectra have different dependencies on the magnetic pulse length allowing for unique on-demand zero-field spectral editing. Precise values for the 15N-1H, 14N-1H, and D-1H coupling constants are extracted from the spectra and the difference in the reduced coupling constants is explained by the secondary isotope effect. Simple symmetric cations such as ammonium do not require expensive isotopic labeling for the observation of J-spectra and, thus, may expand applicability of ZULF NMR spectroscopy in biomedicine and energy storage.Comment: 39 pages, 5 figure

Theoretical description of hyperpolarization formation in the SABRE-relay method

SABRE (Signal Amplification By Reversible Exchange) has become a widely used method for hyper-polarizing nuclear spins, thereby enhancing their Nuclear Magnetic Resonance (NMR) signals by orders of magnitude. In SABRE experiments, the non-equilibrium spin order is transferred from parahydrogen to a substrate in a transient organometallic complex. The applicability of SABRE is expanded by the methodology of SABRE-relay in which polarization can be relayed to a second substrate either by direct chemical exchange of hyperpolarized nuclei or by polarization transfer between two substrates in a second organometallic complex. To understand the mechanism of the polarization transfer and study the transfer efficiency, we propose a theoretical approach to SABRE-relay, which can treat both spin dynamics and chemical kinetics as well as the interplay between them. The approach is based on a set of equations for the spin density matrices of the spin systems involved (i.e., SABRE substrates and complexes), which can be solved numerically. Using this method, we perform a detailed study of polarization formation and analyze in detail the dependence of the attainable polarization level on various chemical kinetic and spin dynamic parameters. We foresee the applications of the present approach for optimizing SABRE-relay experiments with the ultimate goal of achieving maximal NMR signal enhancements for substrates of interest

Possible Applications of Dissolution Dynamic Nuclear Polarization in Conjunction with Zero- to Ultralow-Field Nuclear Magnetic Resonance

The combination of a powerful and broadly applicable nuclear hyperpolarization technique with emerging (near-)zero-field modalities offer novel opportunities in a broad range of nuclear magnetic resonance spectroscopy and imaging applications, including biomedical diagnostics, monitoring catalytic reactions within metal reactors and many others. These are discussed along with a roadmap for future developments.Comment: 12 pages, 5 figure

Zero-field nuclear magnetic resonance of chemically exchanging systems.

Zero- to ultralow-field (ZULF) nuclear magnetic resonance (NMR) is an emerging tool for precision chemical analysis. In this work, we study dynamic processes and investigate the influence of chemical exchange on ZULF NMR J-spectra. We develop a computational approach that allows quantitative calculation of J-spectra in the presence of chemical exchange and apply it to study aqueous solutions of [15N]ammonium (15N[Formula: see text]) as a model system. We show that pH-dependent chemical exchange substantially affects the J-spectra and, in some cases, can lead to degradation and complete disappearance of the spectral features. To demonstrate potential applications of ZULF NMR for chemistry and biomedicine, we show a ZULF NMR spectrum of [2-13C]pyruvic acid hyperpolarized via dissolution dynamic nuclear polarization (dDNP). We foresee applications of affordable and scalable ZULF NMR coupled with hyperpolarization to study chemical exchange phenomena in vivo and in situations where high-field NMR detection is not possible to implement

Rapid hyperpolarization and purification of the metabolite fumarate in aqueous solution

Hyperpolarized fumarate is a promising biosensor for carbon-13 magnetic resonance metabolic imaging. Such molecular imaging applications require nuclear hyperpolarization to attain sufficient signal strength. Dissolution dynamic nuclear polarization is the current state-of-the-art methodology for hyperpolarizing fumarate, but this is expensive and relatively slow. Alternatively, this important biomolecule can be hyperpolarized in a cheap and convenient manner using parahydrogen-induced polarization. However, this process requires a chemical reaction, and the resulting solutions are contaminated with the catalyst, unreacted reagents, and reaction side-product molecules, and are hence unsuitable for use in vivo. In this work we show that the hyperpolarized fumarate can be purified from these contaminants by acid precipitation as a pure solid, and later redissolved to a desired concentration in a clean aqueous solvent. Significant advances in the reaction conditions and reactor equipment allow for formation of hyperpolarized fumarate at ¹³C polarization levels of 30–45%