Nuclear singlet relaxation by scalar relaxation of the second kind in the slow-fluctuation regime

Singlet spin order in spin pairs coupled via non-bonded interactions

Fluorine spin pairs that are constrained in spatial proximity show large scalar spin-spin couplings, despite the atoms being separated by several bonds. This is due to a non-bonded atomic interaction related to partial overlapping of fluorine p-orbitals. In this paper we exploit this phenomenon to create long-lived singlet spin order on the fluorine spin pair. This form of order, which, in this example molecule, is more than an order of magnitude longer than longitudinal order, has the potential to be useful in magnetic resonance imaging and molecular tracing experiments, because of the lack of endogenous fluorine in the human body and the high sensitivity achievable in 19F NMR.

Rapid and Simple 13C-Hyperpolarization by 1H Dissolution Dynamic Nuclear Polarization Followed by an Inline Magnetic Field Inversion

Dissolution dynamic nuclear polarization (dDNP) is a method of choice for preparing hyperpolarized 13C metabolites such as 1-13C-pyruvate used for in vivo applications, including the real-time monitoring of cancer cell metabolism in human patients. The approach consists of transferring the high polarization of electron spins to nuclear spins via microwave irradiation at low temperatures (1.0-1.5 K) and moderate magnetic fields (3.3-7 T). The solid sample is then dissolved and transferred to an NMR spectrometer or MRI scanner for detection in the liquid state. Common dDNP protocols use direct hyperpolarization of 13C spins reaching polarizations of >50% in ∼1-2 h. Alternatively, 1H spins are polarized before transferring their polarization to 13C spins using cross-polarization, reaching polarization levels similar to those of direct DNP in only ∼20 min. However, it relies on more complex instrumentation, requiring highly skilled personnel. Here, we explore an alternative route using 1H dDNP followed by inline adiabatic magnetic field inversion in the liquid state during the transfer. 1H polarizations of >70% in the solid state are obtained in ∼5-10 min. As the hyperpolarized sample travels from the dDNP polarizer to the NMR spectrometer, it goes through a field inversion chamber, which causes the 1H → 13C polarization transfer. This transfer is made possible by the J-coupling between the heteronuclei, which mixes the Zeeman states at zero-field and causes an antilevel crossing. We report liquid-state 13C polarization up to ∼17% for 3-13C-pyruvate and 13C-formate. The instrumentation needed to perform this experiment in addition to a conventional dDNP polarizer is simple and readily assembled.

Deuteron-Decoupled Singlet NMR in Low Magnetic Fields: Application to the Hyperpolarization of Succinic Acid

The reaction of unsaturated substrates with hydrogen gas enriched in the para spin isomer leads to products with a high degree of nuclear singlet spin order. This leads to greatly enhanced NMR signals, with important potential applications such as magnetic resonance imaging (MRI) of metabolic processes. Although parahydrogen-induced polarization has the advantage of being cheap, compact, and mobile, especially when performed in ultralow magnetic fields, efficiency is lost when more than a few protons are involved. This strongly restricts the range of compatible substances. We show that these difficulties may be overcome by a combination of deuteration with the application of a sinusoidally modulated longitudinal field as a well as a transverse rotating magnetic field. We demonstrate a six-fold enhancement in the 13 C hyperpolarization of [1-13 C, 2,3-d2 ]-succinic acid, as compared with standard hyperpolarization methods, applied in the same ultralow field regime.

Multiaxial fields improve SABRE efficiency by preserving hydride order

Signal Amplification By Reversible Exchange (SABRE) and the heteronuclear variant, X-SABRE, increase the sensitivity of magnetic resonance techniques using order derived from reversible binding of para-hydrogen. One current limitation of SABRE is suboptimal polarization transfer over the lifetime of the complex. Here, we demonstrate a multiaxial low-field pulse sequence which allows optimal polarization build-up during a low-field "evolution" pulse, followed by a high-field "mixing" pulse which permits proton decoupling along an orthogonal axis. This preserves the singlet character of the hydrides while allowing exchange to replenish the ligands on the iridium catalyst. This strategy leads to a 2.5-fold improvement over continuous field SABRE SHEATH experimentally which was confirmed with numerical simulation.

Exotic nuclear spin behavior in dendritic macromolecules

Dendrimers are a class of branched, highly symmetric macromolecules that have been shown to be useful for a vast number of different applications. Potential uses as fluorescence sensors, in catalysis and perhaps most importantly in medical applications as drug delivery systems or cytotoxica have been proposed. Herein we report on an exotic behaviour of the nuclear spins in a dendritic macromolecule in the presence of different paramagnetic ions. We show that the stability of the long lived nuclear singlet state, is affected by the presence of Cu(II), whereas other ions did not have any influence at all. This effect could not be observed in the case of a simple tripeptide, in which the nuclear singlet stability was influenced by all investigated paramagnetic ions, a potentially useful effect in the development of Cu(II) selective probes. By adding a fluorescent marker to our molecule we could show that the nuclear singlet multimer (NUSIMER) is taken up by living cells. Furthermore we were able to show that nuclear singlet state NMR can be used to investigate the NUSIMER in the presence of living cells, showing that an application in in vivo NMR can be feasible.

Nuclear singlet relaxation by chemical exchange

The population imbalance between nuclear singlet states and triplet states of strongly coupled spin-1/2 pairs, also known as nuclear singlet order, is well protected against several common relaxation mechanisms. We study the nuclear singlet relaxation of ¹³C pairs in aqueous solutions of 1,2-¹³C₂ squarate over a range of pH values. The ¹³C singlet order is accessed by introducing ¹⁸O nuclei in order to break the chemical equivalence. The squarate dianion is in chemical equilibrium with hydrogen-squarate (SqH^-) and squaric acid (SqH₂) characterized by the dissociation constants pK₁ = 1.5 and pK₂ = 3.4. Surprisingly, we observe a striking increase in the singlet decay time constants T_S when the pH of the solution exceeds ∼10, which is far above the acid-base equilibrium points. We derive general rate expressions for chemical-exchange-induced nuclear singlet relaxation and provide a qualitative explanation of the T_S behavior of the squarate dianion. We identify a kinetic contribution to the singlet relaxation rate constant, which explicitly depends on kinetic rate constants. Qualitative agreement is achieved between the theory and the experimental data. This study shows that infrequent chemical events may have a strong effect on the relaxation of nuclear singlet order.

Centralizer theory for long-lived spin states

Nuclear long-lived spin states represent spin density operator configurations that are exceptionally well protected against spin relaxation phenomena. Their long-lived character is exploited in a variety of Nuclear Magnetic Resonance (NMR) techniques. Despite the growing importance of long-lived spin states in modern NMR, strategies for their identification have changed little over the last decade. The standard approach heavily relies on a chain of group theoretical arguments. In this paper, we present a more streamlined method for the calculation of such configurations. Instead of focusing on the symmetry properties of the relaxation superoperator, we focus on its corresponding relaxation algebra. This enables us to analyze long-lived spin states with Lie algebraic methods rather than group theoretical arguments. We show that the centralizer of the relaxation algebra forms a basis for the set of long-lived spin states. The characterization of the centralizer, on the other hand, does not rely on any special symmetry arguments, and its calculation is straightforward. We outline a basic algorithm and illustrate advantages by considering long-lived spin states for some spin-1/2 pairs and rapidly rotating methyl groups.

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.

Symmetry versus entropy: Long-lived states and coherences

In recent years, new molecular symmetry-based approaches for magnetic resonance have been invented. The implications of these discoveries will be significant for molecular imaging via magnetic resonance, in vitro as well as in vivo, for quantum computing and for other fields. Since the initial observation in 2004 in Southampton that effective spin symmetry can be instilled in a molecule during magnetic resonance experiments, spin states that are resilient to relaxation mechanisms have been increasingly used. Most of these states are related to the nuclear singlet in a pair of J-coupled spins. Tailored relaxation rate constants for magnetization became available in molecules of different sizes and structures, as experimental developments broadened the scope of symmetry-adapted spin states. The ensuing access to timescales longer than the classically-attained ones by circa one order of magnitude allows the study of processes such as slow diffusion or slow exchange that were previously beyond reach. Long-lived states formed by differences between populations of singlets and triplets have overcome the limitations imposed by longitudinal relaxation times (T₁) by factors up to 40. Long-lived coherences formed by superpositions of singlets and triplets have overcome the limit of classical transverse coherence (T₂) by a factor 9. We present here an overview of the development and applications of long-lived states (LLS) and long-lived coherences (LLC's) and considerations on future perspectives.

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.

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.

Application and methodology of dissolution dynamic nuclear polarization in physical, chemical and biological contexts

Dissolution dynamic nuclear polarization (d-DNP) is a versatile method to enhance nuclear magnetic resonance (NMR) spectroscopy. It boosts signal intensities by four to five orders of magnitude thereby providing the potential to improve and enable a plethora of applications ranging from the real-time monitoring of chemical or biological processes to metabolomics and in-cell investigations. This perspectives article highlights possible avenues for developments and applications of d-DNP in biochemical and physicochemical studies. It outlines how chemists, biologists and physicists with various fields of interest can transform and employ d-DNP as a powerful characterization method for their research.

Experimental evidence for the role of paramagnetic oxygen concentration on the decay of long-lived nuclear spin order

Nuclear singlet lifetimes are often dependent on the quantity of paramagnetic oxygen species present in solution, although the extent to which quenching or removing molecular oxygen has on extending singlet lifetimes is typically an unknown factor. Here we investigate the behaviour of the singlet relaxation time constant as a function of the oxygen concentration in solution. An experimental demonstration is presented for a chemically inequivalent proton pair of the tripeptide alanine-glycine-glycine in solution. We introduce a simple methodology to ensure the solution is saturated with predetermined concentrations of oxygen gas prior to measurements of the singlet lifetime. Singlet lifetimes were measured by using the spin-lock induced crossing pulse sequence. We present a linear relationship between the amount of oxygen dissolved in solution and the singlet relaxation rate constant. Singlet relaxation was found to be ∼2.7 times less sensitive to relaxation induced by paramagnetic oxygen compared with longitudinal relaxation. The relaxation behaviour is described by using a model of correlated fluctuating fields. We additionally examine the extension of singlet lifetimes by doping solutions with the chelating agent sodium ascorbate, which scavenges oxygen radicals in solution.

Homonuclear ADAPT: A general preparation route to long-lived nuclear singlet order

We introduce a simple strategy to access and readout nuclear singlet order based on the alternate repetition of hard pulses and delays. We demonstrate the general applicability of the method by accessing nuclear singlet order in spin systems characterized by diverse coupling regimes. We show that the method is highly efficient in the strong-coupling and chemical equivalence regimes, and can overcome some limitations of other well-established and more elaborated pulse sequences. A simulation package is provided which allows the determination of pulse sequence parameters.