Constant-adiabaticity radiofrequency pulses for generating long-lived singlet spin states in NMR

Excitation of long-lived nuclear spin order using spin-locking: a geometrical formalism

Over the last two decades, numerous pulse sequences have been introduced for the excitation of long-lived spin order (LLS) in high fields. The long continuous wave (CW) or adiabatic pulses used in the SLIC and APSOC sequences should remind one of the spin-locking pulses that are used to induce cross-polarization (CP). Dynamics during these spin-lockings in CP experiments are explained through a geometrical formalism. However, the SLIC and APSOC sequences are described in terms of the energy-level picture or in the language of level anti-crossings. Motivated by this analogy, this work presents here a geometrical formalism for the LLS excitation by spin-locking pulses in weakly coupled systems. The formalism is similar to the one used for CP dynamics and reveals new pulse sequences involving CW or adiabatic locking. A similar formalism for the sustaining period of LLS is also provided, which reveals new features of the dynamics and suggests the usage of modulated spin-lockings for proper LLS sustaining. For strong and intermediate regimes, although a simple geometrical formalism seems infeasible, a new pulse sequence that employs a ramp-down adiabatic pulse for both LLS excitation and reconversion to observables in both these regimes is presented here. Given the similarities between LLS excitation and well-developed CP, it may be anticipated that this work would initiate the search for new LLS excitation methods and applications.

Hyperpolarisation criteria in magnetic resonance

Nuclear Magnetic Resonance (NMR) techniques display an inherently low sensitivity due to a small equilibrium magnetisation. Nowadays this issue is easily overcome through the use of hyperpolarisation methods. This however raises the question as to what precisely do we mean by "hyperpolarisation". Recently a formal definition of hyperpolarisation has been given based on the von Neumann entropy of a system. Ideally this definition should conform with the general usage in the magnetic resonance community, where hyperpolarisation is often used synonymously with "larger" NMR signals. Within this article I show that an entropy-based hyperpolarisation criterion does not always conform with the general usage. Based on this observation I introduce an alternative hyperpolarisation criterion utilising the concept of latent polarisation, where latent polarisation is a measure of the highest possible amount of polarisation that may be extracted from a system. I show that a hyperpolarisation criterion based on latent polarisation correlates more strongly with the general usage within the magnetic resonance community. Ultimately however our results show that there are several possible notions of hyperpolarisation, and the choice depends upon the questions of interest.

Radio-Frequency Sweeps at Microtesla Fields for Parahydrogen-Induced Polarization of Biomolecules

Magnetic resonance imaging of ¹³C-labeled metabolites enhanced by parahydrogen-induced polarization (PHIP) enables real-time monitoring of processes within the body. We introduce a robust, easily implementable technique for transferring parahydrogen-derived singlet order into ¹³C magnetization using adiabatic radio frequency sweeps at microtesla fields. We experimentally demonstrate the applicability of this technique to several molecules, including some molecules relevant for metabolic imaging, where we show significant improvements in the achievable polarization, in some cases reaching above 60% nuclear spin polarization. Furthermore, we introduce a site-selective deuteration scheme, where deuterium is included in the coupling network of a pyruvate ester to enhance the efficiency of the polarization transfer. These improvements are enabled by the fact that the transfer protocol avoids relaxation induced by strongly coupled quadrupolar nuclei.

Long-lived states of methylene protons in achiral molecules

In nuclear magnetic resonance (NMR), the lifetimes of long-lived states (LLSs) are exquisitely sensitive to their environment. However, the number of molecules where such states can be excited has hitherto been rather limited. Here, it is shown that LLSs can be readily excited in many common molecules that contain two or more neighboring CH2 groups. Accessing such LLSs does not require any isotopic enrichment, nor does it require any stereogenic centers to lift the chemical equivalence of CH2 protons. LLSs were excited in a variety of metabolites, neurotransmitters, vitamins, amino acids, and other molecules. One can excite LLSs in several different molecules simultaneously. In combination with magnetic resonance imaging, LLSs can reveal a contrast upon noncovalent binding of ligands to macromolecules. This suggests new perspectives to achieve high-throughput parallel drug screening by NMR.

Selective Excitation of Long-Lived Nuclear Spin States

Nuclear magnetization storage, once limited by longitudinal and transverse relaxation lifetimes, T₁ and T₂, can be prolonged by symmetry-adapted nuclear spin order, i.e. long-lived states (LLS) and long-lived coherences (LLC), which have significantly extended relaxation time constants compared to T₁ and T₂, respectively. Excitation and/or detection of LLS currently involves pulses covering wide frequency ranges in high-magnetic-field spectrometers. This leads to excitation of unwanted signals that may overlap and interfere with the resonances of interest. Herein, we present a new pulse sequence that converts longitudinal magnetization to LLS and further to detectable magnetization using only frequency-selective pulses. We demonstrate the suitability of this sequence for different J-coupled spin pairs in dipeptide AlaGly and protein Ubiquitin. The newly developed method is adapted for investigations of LLS in complex systems such as proteins and mixtures of metabolites where selected molecular groups are to be investigated separately.

Recent advances in the application of parahydrogen in catalysis and biochemistry

Nuclear Magnetic Resonance (NMR) spectroscopy and Magnetic Resonance Imaging (MRI) are analytical and diagnostic tools that are essential for a very broad field of applications, ranging from chemical analytics, to non-destructive testing of materials and the investigation of molecular dynamics, to in vivo medical diagnostics and drug research. One of the major challenges in their application to many problems is the inherent low sensitivity of magnetic resonance, which results from the small energy-differences of the nuclear spin-states. At thermal equilibrium at room temperature the normalized population difference of the spin-states, called the Boltzmann polarization, is only on the order of 10-5. Parahydrogen induced polarization (PHIP) is an efficient and cost-effective hyperpolarization method, which has widespread applications in Chemistry, Physics, Biochemistry, Biophysics, and Medical Imaging. PHIP creates its signal-enhancements by means of a reversible (SABRE) or irreversible (classic PHIP) chemical reaction between the parahydrogen, a catalyst, and a substrate. Here, we first give a short overview about parahydrogen-based hyperpolarization techniques and then review the current literature on method developments and applications of various flavors of the PHIP experiment.

Adaptable Singlet-Filtered Nuclear Magnetic Resonance Spectroscopy for Chemical and Biological Applications

Proton nuclear magnetic resonance (¹H NMR) spectroscopy presents a powerful detection tool for studying chemical compositions and molecular structures. In practical chemical and biological applications, ¹H NMR experiments are generally confronted with the challenge of spectral congestions caused by abundant observable components and intrinsic limitations of a narrow frequency distribution range and extensive J coupling splitting. Herein, a one-dimensional (1D) general NMR method is proposed to individually extract the signals of targeted proton groups based on their endogenous spin singlet states excited from J coupling interactions, and it is suitable for high-resolution detections on complex chemical and biological samples. The applicability of the proposed method is demonstrated by experimental observations on chemical solutions containing different coupled components, intact grape tissues subjected to crowded resonances, and in vitro pig brain with various metabolites. Moreover, the proposed method is further exploited for magnetic resonance spectroscopy applications by directly combining the spatial localization module, showing promise in in vivo biological metabolite studies.

Constant-adiabaticity pulse schemes for manipulating singlet order in 3-spin systems with weak magnetic non-equivalence

Parahydrogen-induced polarization (PHIP) is a source of nuclear spin hyperpolarization, and this technique allows for the preparation of biomolecules for in vivo metabolic imaging. PHIP delivers hyperpolarization in the form of proton singlet order to a molecule, but most applications require that a heteronuclear (e.g. ¹³C or ¹⁵N) spin in the molecule is hyperpolarized. Here we present high field pulse methods to manipulate proton singlet order in the [1-¹³C]fumarate, and in particular to transfer the proton singlet order into ¹³C magnetization. We exploit adiabatic pulses, i.e., pulses with slowly ramped amplitude, and use constant-adiabaticity variants: the spin Hamiltonian is varied in such a way that the generalized adiabaticity parameter is time-independent. This allows for faster polarization transfer, and we achieve 96.2% transfer efficiency in thermal equilibrium experiments. We demonstrate this in experiments using hyperpolarization, and obtain 6.8% ¹³C polarization. This work paves the way for efficient hyperpolarization of nuclear spins in a variety of biomolecules, since the high-field pulse sequences allow individual spins to be addressed.

Constant-adiabaticity ultralow magnetic field manipulations of parahydrogen-induced polarization: application to an AA'X spin system

The field of magnetic resonance imaging with hyperpolarized contrast agents is rapidly expanding, and parahydrogen-induced polarization (PHIP) is emerging as an inexpensive and easy-to-implement method for generating the required hyperpolarized biomolecules. Hydrogenative PHIP delivers hyperpolarized proton spin order to a substrate via chemical addition of H₂ in the spin-singlet state, but it is typically necessary to transfer the proton polarization to a heteronucleus (usually ¹³C) which has a longer spin lifetime. Adiabatic ultralow magnetic field manipulations can be used to induce the polarization transfer, but this is necessarily a slow process, which is undesirable since the spins continually relax back to thermal equilibrium. Here we demonstrate two constant-adiabaticity field sweep methods, one in which the field passes through zero, and one in which the field is swept from zero, for optimal polarization transfer on a model AA'X spin system, [1-¹³C]fumarate. We introduce a method for calculating the constant-adiabaticity magnetic field sweeps, and demonstrate that they enable approximately one order of magnitude faster spin-order conversion compared to linear sweeps. The present method can thus be utilized to manipulate nonthermal order in heteronuclear spin systems.

Singlet-Contrast Magnetic Resonance Imaging: Unlocking Hyperpolarization with Metabolism*

Hyperpolarization-enhanced magnetic resonance imaging can be used to study biomolecular processes in the body, but typically requires nuclei such as 13 C, 15 N, or 129 Xe due to their long spin-polarization lifetimes and the absence of a proton-background signal from water and fat in the images. Here we present a novel type of 1 H imaging, in which hyperpolarized spin order is locked in a nonmagnetic long-lived correlated (singlet) state, and is only liberated for imaging by a specific biochemical reaction. In this work we produce hyperpolarized fumarate via chemical reaction of a precursor molecule with para-enriched hydrogen gas, and the proton singlet order in fumarate is released as antiphase NMR signals by enzymatic conversion to malate in D2 O. Using this model system we show two pulse sequences to rephase the NMR signals for imaging and suppress the background signals from water. The hyperpolarization-enhanced 1 H-imaging modality presented here can allow for hyperpolarized imaging without the need for low-abundance, low-sensitivity heteronuclei.

Representation of population exchange at level anti-crossings

A theoretical framework is proposed to describe the spin dynamics driven by coherent spin mixing at level anti-crossings (LACs). We briefly introduce the LAC concept and propose to describe the spin dynamics using a vector of populations of the diabatic eigenstates. In this description, each LAC gives rise to a pairwise redistribution of eigenstate populations, allowing one to construct the total evolution operator of the spin system. Additionally, we take into account that in the course of spin evolution a "rotation" of the eigenstate basis case take place. The approach is illustrated by a number of examples, dealing with magnetic field inversion, cross-polarization, singlet-state nuclear magnetic resonance and parahydrogen-induced polarization.

Robust transformation of singlet order into heteronuclear magnetisation over an extended coupling range

Several important NMR procedures involve the conversion of nuclear singlet order into heteronuclear magnetisation, including some experiments involving long-lived spin states and parahydrogen-induced hyperpolarisation. However most existing sequences suffer from a limited range of validity or a lack of robustness against experimental imperfections. We present a new radio-frequency scheme for the transformation of the singlet order of a chemically-equivalent homonuclear spin pair into the magnetisation of a heteronuclear coupling partner. The proposed radio-frequency (RF) scheme is called gS2hM (generalized singlet-to-heteronuclear magnetisation) and has good compensation for common experimental errors such as RF and static field inhomogeneities. The sequence retains its robustness for homonuclear spin pairs in the intermediate coupling regime, characterised by the in-pair coupling being of the same order of magnitude as the difference between the out-of-pair couplings. This is a substantial improvement to the validity range of existing sequences. Analytical solutions for the pulse sequence parameters are provided. Experimental results are shown for two test cases.

Generalised magnetisation-to-singlet-order transfer in nuclear magnetic resonance

A variety of pulse sequences have been described for converting nuclear spin magnetisation into long-lived singlet order for nuclear spin-1/2 pairs. Existing sequences operate well in two extreme parameter regimes. The magnetisation-to-singlet (M2S) pulse sequence performs a robust conversion of nuclear spin magnetisation into singlet order in the near-equivalent limit, meaning that the difference in chemical shift frequencies of the two spins is much smaller than the spin-spin coupling. Other pulse sequences operate in the strong-inequivalence regime, where the shift difference is much larger than the spin-spin coupling. However both sets of pulse sequences fail in the intermediate regime, where the chemical shift difference and the spin-spin coupling are roughly equal in magnitude. We describe a generalised version of M2S, called gM2S, which achieves robust singlet order excitation for spin systems ranging from the near-equivalence limit well into the intermediate regime. This closes an important gap left by existing pulse sequences. The efficiency of the gM2S sequence is demonstrated numerically and experimentally for near-equivalent and intermediate-regime cases.

Algorithmic cooling of nuclear spins using long-lived singlet order

Algorithmic cooling methods manipulate an open quantum system in order to lower its temperature below that of the environment. We achieve significant cooling of an ensemble of nuclear spin-pair systems by exploiting the long-lived nuclear singlet state, which is an antisymmetric quantum superposition of the "up" and "down" Zeeman states. The effect is demonstrated by nuclear magnetic resonance experiments on a molecular system containing a coupled pair of near-equivalent ¹³C nuclei. The populations of the system are subjected to a repeating sequence of cyclic permutations separated by relaxation intervals. The long-lived nuclear singlet order is pumped well beyond the unitary limit. The pumped singlet order is converted into nuclear magnetization which is enhanced by 21% relative to its thermal equilibrium value.

Generating and sustaining long-lived spin states in 15N,15N'-azobenzene

Long-Lived spin States (LLSs) hold a great promise for sustaining non-thermal spin order and investigating various slow processes by Nuclear Magnetic Resonance (NMR) spectroscopy. Of special interest for such application are molecules containing nearly equivalent magnetic nuclei, which possess LLSs even at high magnetic fields. In this work, we report an LLS in trans-¹⁵N,¹⁵N′-azobenzene. The singlet state of the ¹⁵N spin pair exhibits a long-lived character. We solve the challenging problem of generating and detecting this LLS and further increase the LLS population by converting the much higher magnetization of protons into the ¹⁵N singlet spin order. As far as the longevity of this spin order is concerned, various schemes have been tested for sustaining the LLS. Lifetimes of 17 minutes have been achieved at 16.4 T, a value about 250 times longer than the longitudinal relaxation time of ¹⁵N in this magnetic field. We believe that such extended relaxation times, along with the photochromic properties of azobenzene, which changes conformation upon light irradiation and can be hyperpolarized by using parahydrogen, are promising for designing new experiments with photo-switchable long-lived hyperpolarization.

Polarization of low-γ nuclei by transferring spin order of parahydrogen at high magnetic fields

In this work, we optimize the performance of a previously proposed method for transferring parahydrogen induced polarization to "insensitive" spin-1/2 NMR (Nuclear Magnetic Resonance) nuclei, which have low gyromagnetic ratio and low natural abundance. By optimizing the reaction conditions and pressure of the parahydrogen gas and using adiabatically switched radiofrequency fields we achieve high polarization transfer efficiency and report carbon spin polarization of dimethyl acetylene dicarboxylate reaching 35%, which corresponds to ¹³C NMR signal enhancements of about 43,000 at 9.4 Tesla. Such polarization levels allow one to work with mM concentrations at natural carbon abundance and to detect ¹³C NMR signal in single scan. In combination with a pseudo phase cycle, the polarization transfer method used here also enables efficient suppression of unwanted background signals.

Long live the singlet state!

The field of long-lived states in NMR is reviewed. The relationship of long-lived-state phenomena to those associated with spin isomerism is discussed. A brief overview is given of key developments in the field of long-lived states, including chemical symmetry-switching, the role of magnetic equivalence and magnetic inequivalence, long-lived coherences, hyperpolarized NMR involving long-lived states, quantum-rotor-induced polarization, and parahydrogen-induced hyperpolarization. Current application areas of long-lived states are reviewed, and a peer into the crystal ball reveals future developments in the field.

Polarization transfer via field sweeping in parahydrogen-enhanced nuclear magnetic resonance

We show that in a spin system of two magnetically inequivalent protons coupled to a heteronucleus such as ¹³C, an adiabatic magnetic field sweep, passing through zero field, transfers the proton singlet order into magnetization of the coupled heteronucleus. This effect is potentially useful in parahydrogen-enhanced nuclear magnetic resonance and is demonstrated on singlet-hyperpolarized [1-¹³C]maleic acid, which is prepared via the reaction between [1-¹³C]acetylene dicarboxylic acid and para-enriched hydrogen gas. The magnetic field sweeps are of microtesla amplitudes and have durations on the order of seconds. We show a polarization enhancement by a factor of 10⁴ in the ¹³C spectra of [1-¹³C]maleic acid in a 1.4 T magnetic field.