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

Proton relaxometry of tree leaves at hypogeomagnetic fields

We report on a cross-species proton-relaxometry study in ex vivo tree leaves using nuclear magnetic resonance (NMR) at 7µT. Apart from the intrinsic interest of probing nuclear-spin relaxation in biological tissues at magnetic fields below Earth field, our setup enables comparative analysis of plant water dynamics without the use of expensive commercial spectrometers. In this work, we focus on leaves from common Eurasian evergreen and deciduous tree families: Pinaceae (pine, spruce), Taxaceae (yew), Betulaceae (hazel), Prunus (cherry), and Fagaceae (beech, oak). Using a nondestructive protocol, we measure their effective proton T2 relaxation times as well as track the evolution of water content associated with leaf dehydration. Newly developed “gradiometric quadrature” detection and data-processing techniques are applied in order to increase the signal-to-noise ratio (SNR) of the relatively weak measured signals. We find that while measured relaxation times do not vary significantly among tree genera, they tend to increase as leaves dehydrate. Such experimental modalities may have particular relevance for future drought-stress research in ecology, agriculture, and space exploration

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

Symmetry Constraints on Spin Order Transfer in Parahydrogen-Induced Polarization (PHIP)

It is well known that the association of parahydrogen (pH2) with an unsaturated molecule or a transient metalorganic complex can enhance the intensity of NMR signals; the effect is known as parahydrogen-induced polarization (PHIP). During recent decades, numerous methods were proposed for converting pH2-derived nuclear spin order to the observable magnetization of protons or other nuclei of interest, usually 13C or 15N. Here, we analyze the constraints imposed by the topological symmetry of the spin systems on the amplitude of transferred polarization. We find that in asymmetric systems, heteronuclei can be polarized to 100%. However, the amplitude drops to 75% in A2BX systems and further to 50% in A3B2X systems. The latter case is of primary importance for biological applications of PHIP using sidearm hydrogenation (PHIP-SAH). If the polarization is transferred to the same type of nuclei, i.e., 1H, symmetry constraints impose significant boundaries on the spin-order distribution. For AB, A2B, A3B, A2B2, AA’(AA’) systems, the maximum average polarization for each spin is 100%, 50%, 33.3%, 25%, and 0, respectively, (where A and B (or A’) came from pH2). Remarkably, if the polarization of all spins in a molecule is summed up, the total polarization grows asymptotically with ~1.27N and can exceed 2 in the absence of symmetry constraints (where N is the number of spins). We also discuss the effect of dipole–dipole-induced pH2 spin-order distribution in heterogeneous catalysis or nematic liquid crystals. Practical examples from the literature illustrate our theoretical analysis