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In this lecture, a fast overview of the formalism used in Nuclear Magnetic Resonance is provided, with a stress on the density matrix approach. Its equivalence to the classical derivation for particular spin systems is shown. The different interactions which are usually encountered are introduced. Finally, the case of randomly time-dependent interactions inducing relaxation is addressed.

A precise measurement of the interglycosidic distances in the cyclic osmoregulated periplasmic glucans of Burkholderia solanacearum was obtained using the off-resonance ROESY technique. The zone of lowest energy was the site of all beta-(1-2) linkages. The alternating pattern of the chemical shifts of the H1 and C2 atoms flanking the glycosidic beta-(1-2) linkage correlates with the observed trend of chemical shift values. These results represent the initial step toward a detailed experimental model of cyclic glucans, which may clarify their biological role.

Nuclear spin noise spectroscopy in the absence of radio frequency pulses was studied under the influence of pulsed field gradients (PFGs) on pure and mixed liquids. Under conditions where the radiation-damping-induced line broadening is smaller than the gradient-dependent inhomogeneous broadening, echo responses can be observed in difference spectra between experiments employing pulsed field gradient pairs of the same and opposite signs. These observed spin noise gradient echoes (SNGEs) were analyzed through a simple model to describe the effects of transient phenomena. Experiments performed on high-resolution nuclear magnetic resonance (NMR) probes demonstrate how refocused spin noise behaves and how it can be exploited to determine sample properties. In bulk liquids and their mixtures, transverse relaxation times and translational diffusion constants can be determined from SNGE spectra recorded following tailored sequences of magnetic field gradient pulses., Competing Interests: The contact author has declared that neither they nor their co-authors have any competing interests., (Copyright: © 2021 Victor V. Rodin et al.)

The availability of a benchtop nuclear magnetic resonance (NMR) spectrometer, of low cost and easily transportable, can allow detection of low quantities of biosensors, provided that hyperpolarized species are used. Here we show that the micromolar threshold can easily be reached by employing laser-polarized xenon and cage molecules reversibly hosting it. Indirect detection of caged xenon is made via chemical exchange, using ultra-fast Z spectroscopy based on spatio-temporal encoding. On this non-dedicated low-field spectrometer, several ideas are proposed to improve the signal., Competing Interests: The authors declare that they have no conflict of interest., (Copyright: © 2021 Kévin Chighine et al.)

The detection of minor species in the presence of large amounts of similar main components remains a key challenge in analytical chemistry, for instance, to obtain isotopic fingerprints. As an alternative to the classical NMR scheme based on coherent excitation and detection, here we introduce an approach based on spin-noise detection. Chemical shifts and transverse relaxation rates are determined using only the detection circuit. Thanks to a nonlinear effect in mixtures with small chemical shift dispersion, small signals on top of a larger one can be observed with increased sensitivity as bumps on a dip; the latter being the signature of the main magnetization. Experimental observations are underpinned by an analytical theory: the coupling between the magnetization and the coil provides an amplified detection capability of both small static magnetic field inhomogeneities and small NMR signals. This is illustrated by two-bond 12 C/ 13 C isotopic measurements.

The theoretical shapes of nuclear spin-noise spectra in NMR are derived by considering a receiver circuit with finite preamplifier input impedance and a transmission line between the preamplifier and the probe. Using this model, it becomes possible to reproduce all observed experimental features: variation of the NMR resonance linewidth as a function of the transmission line phase, nuclear spin-noise signals appearing as a "bump" or as a "dip" superimposed on the average electronic noise level even for a spin system and probe at the same temperature, pure in-phase Lorentzian spin-noise signals exhibiting non-vanishing frequency shifts. Extensive comparisons to experimental measurements validate the model predictions, and define the conditions for obtaining pure in-phase Lorentzian-shape nuclear spin noise with a vanishing frequency shift, in other words, the conditions for simultaneously obtaining the spin-noise and frequency-shift tuning optima.

Three optimum conditions for the tuning of NMR probes are compared: the conventional tuning optimum, which is based on radio-frequency pulse efficiency, the spin noise tuning optimum based on the line shape of the spin noise signal, and the newly introduced frequency shift tuning optimum, which minimizes the frequency pushing effect on strong signals. The latter results if the radiation damping feedback field is not in perfect quadrature to the precessing magnetization. According to the conventional RLC (resistor-inductor-capacitor) resonant circuit model, the optima should be identical, but significant deviations are found experimentally at low temperatures, in particular on cryogenically cooled probes. The existence of different optima with respect to frequency pushing and spin noise line shape has important consequences on the nonlinearity of spin dynamics at high polarization levels and the implementation of experiments on cold probes., (© 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

Numerical simulations based on microscopic approach are used to explore the spin dynamics encountered in the recently reported hyperpolarized (129)Xe NMR maser [D. J. Y. Marion, G. Huber, P. Berthault, and H. Desvaux, ChemPhysChem 9, 1395-1401 (2008)] where series of amplitude modulated rf emissions are observed. The integration of the dynamic features of the electronic detection circuit in the present simulations, based on non-linear Maxwell-Bloch differential equations with dipole-dipole interactions, allows us to prove that the experimentally observed extremely random amplitude modulations crucially require the long-distance dipolar couplings between the nuclear spins with the feedback field acting as an amplifier. The massive dipolar couplings act, when the magnetization is largely tilted off the longitudinal axis, as an apparent transverse self-relaxation mechanism which destroys coherence. This, in particular, explains why the final magnetization after emissions can still be opposite to the magnetic field direction, i.e., being in an unstable state.

When NMR lines overlap and at least one of them is affected by radiation damping, the resonance line shapes of all lines are no longer Lorentzian. We report the appearance of narrow signal distortions, which resemble hole-burnt spectra. This new experimental phenomenon facilitates the detection of tiny signals hidden below the main resonance. Theoretical analysis based on modified Maxwell-Bloch equations shows that the presence of strong transverse magnetization creates a feedback through the coil, which influences the magnetization of all spins with overlapping resonance lines. In the time domain this leads to cross-precession terms between magnetization densities, which ultimately cause non-linear behavior. Numerical simulations corroborate this interpretation., (Copyright © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

We show that the differentiation between internal and external compartments of various biological cells in suspension can be made via simple NMR spectra of hyperpolarized (129) Xe. The spectral separation between the signals of (129) Xe in these two compartments is already known for red blood cells, because of the strong interaction of the noble gas with hemoglobin. The observation of two separate peaks in the 200-ppm region can be seen with both eukaryotic and prokaryotic cells, some of which are not known to contain paramagnetic proteins in large quantities. Using different experiments in which the cells are lysed, swell or are blocked in G2 phase, we demonstrate that the low-field-shifted peak observed corresponds to xenon in the aqueous pool inside the cells and not in the membranes. The presence of this additional peak is a clear indication of cell integrity, and its integration allows the quantification of the total cell volume. The relaxation time of intracellular xenon is sufficiently long to open up promising perspectives for cell characterization. The exchange time between the inner and outer cell compartments (on the order of 30 ms) renders possible the targeting of intracellular receptors, whereas the observation of chemical shift variations represents a method of revealing the presence of toxic species in the cells., (Copyright © 2011 John Wiley & Sons, Ltd.)

For detection of biological events in vitro, sensors using hyperpolarized (129)Xe NMR can become a powerful tool, provided the approach can bridge the gap in sensitivity. Here we propose constructs based on the non-selective grafting of cryptophane precursors on holo-transferrin. This biological system was chosen because there are many receptors on the cell surface, and endocytosis further increases this density. The study of these biosensors with K562 cell suspensions via fluorescence microscopy and (129)Xe NMR indicates a strong interaction, as well as interesting features such as the capacity of xenon to enter the cryptophane even when the biosensor is endocytosed, while keeping a high level of polarization. Despite a lack of specificity for transferrin receptors, undoubtedly due to the hydrophobic character of the cryptophane moiety that attracts the biosensor into the cell membrane, these biosensors allow the first in-cell probing of biological events using hyperpolarized xenon., (Copyright © 2011 Elsevier Ltd. All rights reserved.)