Sample convection in liquid-state NMR: why it is always with us, and what we can do about it

To flame-seal or not to flame-seal NMR tubes: The role of liquid-vapor equilibria on the accuracy of variable temperature experiments

In NMR experiments, it is crucial to control the temperature of the sample, especially when measuring kinetic parameters. Usually, it takes 2 to 5 min for the temperature of the sample inside the NMR probe to stabilize at a fixed value set for the experiment. However, the NMR sample tubes are flame-sealed in some cases, such as when working with volatile solvents, atmosphere-sensitive samples, or calibration samples for long-term use. When these samples are placed inside the NMR probe, the spectrometer controls the lower portion (liquid phase) of the NMR sample tube with a gas flow at a fixed temperature, while the upper portion (vapor) is at ambient temperature. This probe design creates a unique temperature gradient across the sample, leading to vapor pressure build-up, particularly inside a sealed NMR tube. By analyzing the temperature-dependent spectral line shape changes of a chemical exchange process, we report that under standard experimental conditions, the sample temperature can take up to 2 to 3 h (instead of minutes) to stabilize. The time scale of the liquid-vapor equilibrium process is much slower, with a half-life exceeding 35 min, in contrast to the 2-min duration required to obtain each spectrum. This phenomenon is exclusively due to the liquid-vapor equilibrium process of the flame-sealed NMR tube and is not observable otherwise.

Size Determination of Organic Cages by Diffusion NMR Spectroscopy

Reliable structure elucidation of covalent organic cage compounds remains challenging as routine analysis might leave ambiguities. Diffusion-ordered NMR spectroscopy (DOSY) allows insight into the molecular size and mass of the species present in solution, but a systematic evaluation of the diffusion behavior for cage assemblies is rarely considered. Here we report the synthesis of four series of covalent organic cages based on tribenzotriquinacenes and diboronic acids with varying geometry and exohedral substituents. We provide a guideline for the consistent measurement of diffusion coefficients from 1 H-DOSY NMR spectroscopy, which was utilized to study the diffusion behavior for the whole set of cages and selected examples from the literature. For structurally similar cages, a linear correlation between the solvodynamic volume and the molecular mass allows precise size determination. For more complex systems, multiple parameters, such as window size or rigid exohedral functionalization. further modulate cage diffusion in solution.

Recovering sensitivity lost through convection in pure shift NMR

Practical pure shift NMR experiments, especially on instruments equipped with cryoprobes, can sometimes give very disappointing results. Here we show for the first time that this is a consequence of signal loss due to sample convection, and demonstrate a simple adjustment to common pure shift NMR experiments that restores the lost signal.

Theoretical analysis of flow effects in spatially encoded diffusion NMR

The measurement of translational diffusion coefficients by nuclear magnetic resonance (NMR) spectroscopy is essential in a broad range of fields, including organic, inorganic, polymer, and supramolecular chemistry. It is also a powerful method for mixture analysis. Spatially encoded diffusion NMR (SPEN DNMR)" is a time efficient technique to collect diffusion NMR data, which is particularly relevant for the analysis of samples that evolve in time. In many cases, motion other than diffusion is present in NMR samples. This is, for example, the case of flow NMR experiments, such as in online reaction monitoring and in the presence of sample convection. Such motion is deleterious for the accuracy of DNMR experiments in general and for SPEN DNMR in particular. Limited theoretical understanding of flow effects in SPEN DNMR experiments is an obstacle for their broader experimental implementation. Here, we present a detailed theoretical analysis of flow effects in SPEN DNMR and of their compensation, throughout the relevant pulse sequences. This analysis is validated by comparison with numerical simulation performed with the Fokker-Planck formalism. We then consider, through numerical simulation, the specific cases of constant, laminar, and convection flow and the accuracy of SPEN DNMR experiments in these contexts. This analysis will be useful for the design and implementation of fast diffusion NMR experiments and for their applications.

Identification of Distinct Soluble States During Fibril Formation Using Multilinear Analysis of NMR Diffusion Data

Protein misfolding and self-assembling into amyloid structures are associated with a number of diseases. Characterization of protein amyloid formation reactions is a challenging task as transient populations of multiple species are involved. Here we outline a method for identification and characterization of the individual soluble states during protein amyloid formation. The method combines NMR translational diffusion measurements with multilinear data analysis.

A Simple Elimination of the Thermal Convection Effect in NMR Diffusiometry Experiments

Thermal convection is always present when the temperature of an NMR experiment is different from the ambient one. Most often, it falsifies the value of the diffusion coefficient determined by NMR diffusiometry using a PGSE NMR experiment. In spite of common belief, it acts not only at higher temperatures but also at temperatures lower than in the laboratory. Sodium alkyl-sulfate monomers and micelles in D₂O solvent were used as model molecules measured at T = 319 K in order to show that thermal convection sometimes remains hidden in experiments. In this paper, we demonstrate that the increase in apparent diffusion coefficient with increasing diffusion time is a definite indicator of thermal convection. Extrapolation to zero diffusion time can also be used to obtain the real diffusion coefficient, likewise applying the less sensitive pulse sequences designed for flow compensation or the expensive hardware, e.g., sapphire or Shigemi NMR tubes, to decrease the temperature gradient. Further, we show experiments illustrating the effect of a long diffusion time in which the periodic changes of the echo intensity with gradient strength appear as predicted by theories.

Giving Pure Shift NMR Spectroscopy a REST─Ultrahigh-Resolution Mixture Analysis

Most interesting problems in chemistry, biology, and pharmacy involve mixtures. However, analysis of such mixtures by NMR remains a challenge, often requiring the mixture components to be physically separated before analysis. A variety of methods have been proposed that exploit species-specific properties such as diffusion and relaxation to distinguish between the signals of different components in a mixture without the need for laborious separation. However, these methods can struggle to distinguish between components when signals overlap. Here, we exploit the relaxation properties of selected nuclei to distinguish between different components of a mixture while using pure shift methods to increase spectral resolution by up to an order of magnitude, greatly reducing signal overlap. The advantages of the new method are demonstrated in a mixture of d-xylose and l-arabinose, distinguishing unambiguously between the five major species present.

Quantitative Interpretation of Protein Diffusion Coefficients in Mixed Protiated-Deuteriated Aqueous Solvents

Diffusion-ordered nuclear magnetic resonance (NMR) spectroscopy is widely used for the analysis of mixtures, dispersing the signals of different species in a two-dimensional spectrum according to their diffusion coefficients. However, interpretation of these diffusion coefficients is typically purely qualitative, for example, to deduce which species are bigger or smaller. In studies of proteins in solution, important questions concern the molecular weight of the proteins, the presence or absence of aggregation, and the degree of folding. The Stokes–Einstein Gierer–Wirtz estimation (SEGWE) method has been previously developed to simplify the complex relationship between diffusion coefficient and molecular mass, allowing the prediction of a species’ diffusion coefficient in a pure solvent based on its molecular weight. Here, we show that SEGWE can be extended to successfully predict both peptide and protein diffusion coefficients in mixed protiated–deuteriated water samples and, hence, distinguish effectively between globular and disordered proteins.

Pulse-field gradient nuclear magnetic resonance of protein translational diffusion from native to non-native states

Hydrodynamic radii (R_h -values) calculated from diffusion coefficients measured by pulse-field-gradient nuclear magnetic resonance are compared for folded and unfolded proteins. For native globular proteins, the R_h -values increase as a power of 0.35 with molecular size, close to the scaling factor of 0.33 predicted from polymer theory. Unfolded proteins were studied under four sets of conditions: in the absence of denaturants, in the presence of 6 M urea, in 95% dimethyl sulfoxide (DMSO), and in 40% hexafluoroisopropanol (HFIP). Scaling factors under all four unfolding conditions are similar (0.49-0.53) approaching the theoretical value of 0.60 for a fully unfolded random coil. Persistence lengths are also similar, except smaller in 95% DMSO, suggesting that the polypeptides are more disordered on a local scale with this solvent. Three of the proteins in our unfolded set have an asymmetric sequence-distribution of charged residues. While these proteins behave normally in water and 6 M urea, they give atypically low R_h -values in 40% HFIP and 95% DMSO suggesting they are forming electrostatic hairpins, favored by their asymmetric sequence charge distribution and the low dielectric constants of DMSO and HFIP. While diffusion-ordered NMR spectroscopy can separate small molecules, we show a number of factors combine to make protein-sized molecules much more difficult to resolve in mixtures. Finally, we look at the temperature dependence of apparent diffusion coefficients. Small molecules show a linear temperature response, while large proteins show abnormally large apparent diffusion coefficients at high temperatures due to convection, suggesting diffusion reference standards are only useful near 25°C.

Mechanistic analysis by NMR spectroscopy: A users guide

A 'principles and practice' tutorial-style review of the application of solution-phase NMR in the analysis of the mechanisms of homogeneous organic and organometallic reactions and processes. This review of 345 references summarises why solution-phase NMR spectroscopy is uniquely effective in such studies, allowing non-destructive, quantitative analysis of a wide range of nuclei common to organic and organometallic reactions, providing exquisite structural detail, and using instrumentation that is routinely available in most chemistry research facilities. The review is in two parts. The first comprises an introduction to general techniques and equipment, and guidelines for their selection and application. Topics include practical aspects of the reaction itself, reaction monitoring techniques, NMR data acquisition and processing, analysis of temporal concentration data, NMR titrations, DOSY, and the use of isotopes. The second part comprises a series of 15 Case Studies, each selected to illustrate specific techniques and approaches discussed in the first part, including in situ NMR (^1/2H, ^10/11B, ¹³C, ¹⁵N, ¹⁹F, ²⁹Si, ³¹P), kinetic and equilibrium isotope effects, isotope entrainment, isotope shifts, isotopes at natural abundance, scalar coupling, kinetic analysis (VTNA, RPKA, simulation, steady-state), stopped-flow NMR, flow NMR, rapid injection NMR, pure shift NMR, dynamic nuclear polarisation, ¹H/¹⁹F DOSY NMR, and in situ illumination NMR.

Rapid Online Analysis of Photopolymerization Kinetics and Molecular Weight Using Diffusion NMR

Online, high-throughput molecular weight analysis of polymerizations is rare, with most studies relying on tedious sampling techniques and batchwise postanalysis. The ability to track both monomer conversion and molecular weight evolution in real time could underpin precision polymer development and facilitate study of rapid polymerization reactions. Here, we use a single time-resolved diffusion nuclear magnetic resonance (NMR) experiment to simultaneously study the kinetics and molecular weight evolution during a photopolymerization, with in situ irradiation inside the NMR instrument. As a model system, we used a photoinduced electron transfer reversible addition-fragmentation chain transfer (PET-RAFT) polymerization. The data allow diffusion coefficients and intensities to be calculated every 14 s from which the polymer size and monomer conversion can be extracted. Key to this approach is (1) the use of shuffled gradient amplitudes in the diffusion NMR experiment to access reactions of any rate, (2) the addition of a relaxation agent to increase achievable time resolution and, (3) a sliding correction that accounts for viscosity changes during polymerization. Diffusion NMR offers a uniquely simple, translatable handle for online monitoring of polymerization reactions.

Extension and improvement of the methanol-d4 NMR thermometer calibration

NMR thermometers are a convenient way to determine the temperature inside the sample of an NMR spectrometer. They rely on signals with strongly temperature-dependent chemical shifts, often of OH groups; 99.8% perdeuterated methanol is an established example which is particularly well suited for modern, high-sensitivity spectrometers, but it is so far calibrated only in the range of 282 to 330 K. In this work, we extend this calibration to the entire liquid range of methanol, 175 to 338 K. Additionally, we use a temperature sensor calibrated traceably to the International Temperature Scale (ITS-90) and accounted for the magnetic field effect on the sensor, yielding a more accurate calibration curve with an uncertainty (2σ) varying between 25 and 190 mK.

Molecular Diffusivity of Click Reaction Components: The Diffusion Enhancement Question

Micrometer-sized objects are widely known to exhibit chemically driven motility in systems away from equilibrium. Experimental observation of reaction-induced motility or enhancement in diffusivity at the much shorter length scale of small molecules is, however, still a matter of debate. Here, we investigate the molecular diffusivity of reactants, catalyst, and product of a model reaction, the copper-catalyzed azide-alkyne cycloaddition click reaction, and develop new NMR diffusion approaches that allow the probing of reaction-induced diffusion enhancement in nanosized molecular systems with higher accuracy than the state of the art. Following two different approaches that enable the accounting of time-dependent concentration changes during NMR experiments, we closely monitored the diffusion coefficient of reaction components during the reaction. The reaction components showed distinct changes in the diffusivity: while the two reactants underwent a time-dependent decrease in their diffusivity, the diffusion coefficient of the product gradually increased and the catalyst showed only slight diffusion enhancement within the range expected for reaction-induced sample heating. The decrease in diffusion coefficient of the alkyne, one of the two reactants of click reaction, was not reproduced during its copper coordination when the second reactant, azide, was absent. Our results do not support the catalysis-induced diffusion enhancement of the components of the click reaction and, instead, point to the role of a relatively large intermediate species within the reaction cycle with diffusivity lower than that of both the reactants and product molecule.

Optimisation of spatially-encoded diffusion-ordered NMR spectroscopy for the analysis of mixtures

Diffusion-ordered NMR spectroscopy (DOSY NMR) is a widely used method for the analysis of mixtures. It can be used to separate the spectra of a mixture's components and to analyse interactions. The classic implementation of DOSY experiments, based on an incrementation of the diffusion-encoding gradient area, requires several minutes or more to collect a 2D data set. Spatially-encoded (SPEN) DOSY makes it possible to collect a complete data set in less than 1 s, by spatial parallelisation of the effective gradient area. While several short descriptions of SPEN DOSY experiments have been reported, a thorough characterisation of its features and its practical use is missing, and this hinders the use of the method. Here, we present the unusual principles and implementation of the SPEN DOSY experiment, an understanding of which is useful to make optimal use of the method. The encoding and acquisition steps are described, and the parameter relations that govern the setup of SPEN DOSY experiments are discussed. The influence of key parameters, including on sensitivity, is illustrated experimentally on mixtures of small molecules. This study should be useful for the setup of SPEN DOSY experiments, which are particularly useful for systems that evolve in time.

Perturbing dimer interactions and allosteric communication modulates the immunosuppressive activity of human galectin-7

The design of allosteric modulators to control protein function is a key objective in drug discovery programs. Altering functionally essential allosteric residue networks provides unique protein family subtype specificity, minimizes unwanted off-target effects, and helps avert resistance acquisition typically plaguing drugs that target orthosteric sites. In this work, we used protein engineering and dimer interface mutations to positively and negatively modulate the immunosuppressive activity of the proapoptotic human galectin-7 (GAL-7). Using the PoPMuSiC and BeAtMuSiC algorithms, mutational sites and residue identity were computationally probed and predicted to either alter or stabilize the GAL-7 dimer interface. By designing a covalent disulfide bridge between protomers to control homodimer strength and stability, we demonstrate the importance of dimer interface perturbations on the allosteric network bridging the two opposite glycan-binding sites on GAL-7, resulting in control of induced apoptosis in Jurkat T cells. Molecular investigation of G16X GAL-7 variants using X-ray crystallography, biophysical, and computational characterization illuminates residues involved in dimer stability and allosteric communication, along with discrete long-range dynamic behaviors involving loops 1, 3, and 5. We show that perturbing the protein-protein interface between GAL-7 protomers can modulate its biological function, even when the overall structure and ligand-binding affinity remains unaltered. This study highlights new avenues for the design of galectin-specific modulators influencing both glycan-dependent and glycan-independent interactions.

Signal-to-noise ratio in diffusion-ordered spectroscopy: how good is good enough?

Diffusion-ordered NMR spectroscopy (DOSY) constructs multidimensional spectra displaying signal strength as a function of Larmor frequency and of diffusion coefficient from experimental measurements using pulsed field gradient spin or stimulated echoes. Peak positions in the diffusion domain are determined by diffusion coefficients estimated by fitting experimental data to some variant of the Stejskal-Tanner equation, with the peak widths determined by the standard error estimated in the fitting process. The accuracy and reliability of the diffusion domain in DOSY spectra are therefore determined by the uncertainties in the experimental data and thus in part by the signal-to-noise ratio of the experimental spectra measured. Here the Cramér-Rao lower bound, Monte Carlo methods, and experimental data are used to investigate the relationship between signal-to-noise ratio, experimental parameters, and diffusion domain accuracy in 2D DOSY experiments. Experimental results confirm that sources of error other than noise put an upper limit on the improvement in diffusion domain accuracy obtainable by time averaging.

Principal Component Analysis of 1D 1H Diffusion Edited NMR Spectra of Protein Therapeutics

The one-dimensional (1D) diffusion edited proton NMR method, Protein Fingerprint by Lineshape Enhancement (PROFILE) has been demonstrated to be suitable for higher order structure (HOS) characterization of protein therapeutics including monoclonal antibodies. Recent reports in the literature have demonstrated its advantages for HOS characterization over traditional methods such as circular dichroism and Fourier-transform infrared spectroscopy. Previously, we have demonstrated that the PROFILE method is complementary with high resolution 2D methyl correlated NMR methods and how both may be deployed as a multi-modal platform to further the utility of NMR for HOS characterization. A major limitation of the PROFILE method remains its need for high signal to noise data due to its reliance on convolution difference processing and linear correlation metrics to assess spectral similarity. Here we present an alternative method for analyzing 1D diffusion edited spectra, which overcomes this limitation by using nonlinear iterative partial least squares (NIPALS) principal component analysis, and which we dub PROtein Fingerprint Observed Using NIPALS Decomposition (PROFOUND). We demonstrate that results from the PROFOUND method are robust with respect to instrument, operator and in the presence of high experimental noise and how it may be employed to provide quantitative assessment of spectral similarity.

Single-scan measurements of nuclear spin singlet order decay rates

Measurements of singlet spin order decay rates are time consuming due to the long-lived nature of this form of order and the typical pseudo-2D mode of acquisition. Additionally, this acquisition modality is not ideal for experiments run on hyperpolarized order because of the single-shot nature of hyperpolarization techniques. We present a methodology based on spatial encoding that not only significantly reduces the duration of these experiments but also confers compatibility using spin hyperpolarization techniques. The method condenses in a single shot the variable delay array used to measure decay rates in conventional pseudo-2D relaxation experiments. This results in a substantial time saving factor and, more importantly, makes the experiment compatible with hyperpolarization techniques since only a single hyperpolarized sample is required. Furthermore, the presented method, besides offering savings on time and costs, avoids reproducibility concerns associated with repetition in the hyperpolarization procedure. The method accelerates the measurement and characterization of singlet order decay times, and, when coupled with hyperpolarization techniques, can facilitate the quest for systems with very long decay times.

Using NMR to Test Molecular Mobility during a Chemical Reaction

We evaluate critically the use of pulsed gradient spin-echo nuclear magnetic resonance to measure molecular mobility during chemical reactions. With raw NMR spectra available in a public depository, we confirm the boosted mobility during the click chemical reaction (Wang et al. Science 2020 369, 537-541) regardless of the order of magnetic field gradient (linearly increasing, linearly decreasing, random sequence). We also confirm boosted mobility for the Diels-Alder chemical reaction. The conceptual advantage of the former chemical system is that a constant reaction rate implies a constant catalyst concentration, whereas that of the latter is the absence of a paramagnetic catalyst, precluding paramagnetism as an objection to the measurements. The data and discussion in this paper show the reliability of experiments when one avoids convection, allows decay of nuclear spin magnetization between successive pulses and recovery of its intensity between gradients, and satisfies quasi-steady state during the time window to acquire each datum. Especially important is to make comparisons on the time scale of the actual chemical reaction kinetics. We discuss possible sources of mistaken conclusions that are desirable to avoid.

Engineering aspects of FlowNMR spectroscopy setups for online analysis of solution-phase processes

In this article we review some fundamental engineering concepts and evaluate components and materials required to assemble and operate safe and effective FlowNMR setups that reliably generate meaningful results.

Exchange-modified DOSY experiments. the use of chiral solvating agents and lanthanide shift reagents as matrices

(S)-BINOL and Eu(fod)₃ were tried as matrices to improve DOSY performance and D^t and MW prediction power on small organic molecules.

Controlled Diffusion of Photoswitchable Receptors by Binding Anti-electrostatic Hydrogen-Bonded Phosphate Oligomers

Dihydrogen phosphate anions are found to spontaneously associate into anti-electrostatic oligomers via hydrogen bonding interactions at millimolar concentrations in DMSO. Diffusion NMR measurements supported formation of these oligomers, which can be bound by photoswitchable anion receptors to form large bridged assemblies of approximately three times the volume of the unbound receptor. Photoisomerization of the oligomer-bound receptor causes a decrease in diffusion coefficient of up to 16%, corresponding to a 70% increase in effective volume. This new approach to external control of diffusion opens prospects in controlling molecular transport using light.

The self-diffusion of polymethylsilsesquioxane (PMSSO) dendrimers in diluted solutions and melts

Recently developed non-functional derivatives of polymethylsilsesquioxane (PMSSO) dendrimers of the first to fifth generation were characterized by 1H, 13C and 29Si NMR spectroscopy. The self-diffusion and NMR relaxation of PMSSO dendrimers in dilute solutions of toluene and melts were investigated in a wide temperature range (-50-80 °C). The hydrodynamic radii of dendrimers were determined from the self-diffusion coefficients measured in diluted solutions according to the Stokes-Einstein equation. The hydrodynamic radius of PMSSO dendrimers as a function of molecular mass follows a power law with the scaling exponent of 0.32 ± 0.02 in the investigated temperature range. The temperature dependences of the self-diffusion coefficients of dendrimers were described by the Arrhenius-type equation. The activation energies of self-diffusion of dendrimers in diluted toluene solutions are identical for different generations while the dependence of activation energy for dendrimers in melts shows a maximum for the third generation (G3) dendrimer. Taking into account the absence of specific interactions in PMSSO dendrimer melts the observed behavior was ascribed to the manifestation of interpenetration of dendrimer molecules. For low generations (G1 and G2) the short length of the branches does not considerably affect the translational diffusion while for higher generations (G4 and G5) the densification of the structure prevents significant interpenetration.

A temperature-controlled sample shuttle for field-cycling NMR

We present a design for a temperature-controlled sample shuttle for use in NMR measurements at variable magnetic field strength. Accurate temperature control was achieved using a mixture of water-ethylene glycol as a heat transfer fluid, reducing temperature gradients across the sample to < 0.05 °C and minimising convection. Using the sample shuttle, we show how the longitudinal (T₁) and singlet order (T_S) relaxation time constants were measured for two molecules capable of supporting long-lived states, with new record lifetimes observed at low field and above ambient temperatures.

Boosted molecular mobility during common chemical reactions

Mobility of reactants and nearby solvent is more rapid than Brownian diffusion during several common chemical reactions when the energy release rate exceeds a threshold. Screening a family of 15 organic chemical reactions, we demonstrate the largest boost for catalyzed bimolecular reactions, click chemistry, ring-opening metathesis polymerization, and Sonogashira coupling. Boosted diffusion is also observed but to lesser extent for the uncatalyzed Diels-Alder reaction, but not for substitution reactions SN1 and SN2 within instrumental resolution. Diffusion coefficient increases as measured by pulsed-field gradient nuclear magnetic resonance, whereas in microfluidics experiments, molecules in reaction gradients migrate “uphill” in the direction of lesser diffusivity. This microscopic consumption of energy by chemical reactions transduced into mechanical motion presents a form of active matter.

The interpretation of small molecule diffusion coefficients: Quantitative use of diffusion-ordered NMR spectroscopy

Measuring accurate molecular self-diffusion coefficients, D, by nuclear magnetic resonance (NMR) techniques has become routine as hardware, software and experimental methodologies have all improved. However, the quantitative interpretation of such data remains difficult, particularly for small molecules. This review article first provides a description of, and explanation for, the failure of the Stokes-Einstein equation to accurately predict small molecule diffusion coefficients, before moving on to three broadly complementary methods for their quantitative interpretation. Two are based on power laws, but differ in the nature of the reference molecules used. The third addresses the uncertainties in the Stokes-Einstein equation directly. For all three methods, a wide range of examples are used to show the range of chemistry to which diffusion NMR can be applied, and how best to implement the different methods to obtain quantitative information from the chemical systems studied.

An MRI-based switched gradient impulse response characterization method with uniform eigenmode excitation

Switching gradients generate eddy currents and mechanical vibrations of the gradient assembly causing errors in the gradient time integrals. This results in image distortions in k-space and inaccuracies in q-space imaging. The purpose of this work is to develop an MRI based unbiased measurement of the switched gradient impulse response function (sGIRF). A new gradient pattern, called the Tukey windowed Shifted Sine-Integral (Tw-SSI) pulse, is introduced to excite the gradient eigenmodes uniformly over a user-defined bandwidth. A 3D MRI-based method with Hadamard encoding was developed to map the spatiotemporal magnetic field generated after the excitation pulse to obtain the sGIRF for all the three gradient axes simultaneously. Compared to an energy-equivalent traditional trapezoidal pulse, the Tw-SSI pulse is able to excite the weak bandlimited cross-terms of the sGIRF by uniformly distributing the energy across eigenmodes. The developed field mapping method is sensitive enough to capture both the direct and cross-terms in the sGIRF. The various mechanical resonant modes of the gradient coils are also revealed, which were found to last longer than eddy currents in the shielded gradient coil studied. Tunable Tw-SSI pulse offers the flexibility to perform unbiased sGIRF measurements over a bandwidth of interest. Rapid MRI field mapping can be easily implemented in any MRI system. The method may be used to perform gradient pre-emphasis, to evaluate new gradient coil designs, and to characterize higher order shims.

Phase contrast MRI of creeping flows using stimulated echo

Creeping flows govern many important physiological phenomena such as elevated interstitial fluid flows in tumors, glymphatic flows in the brain, among other applications. However, few methods exist to measure such slow flows non-invasively in optically opaque biological tissues in vivo. Phase-contrast MRI is a velocimetry technique routinely used in the clinic to measure fast flows in biological tissues, such as blood and cerebrospinal fluid (CSF), in the order of cm/s. Use of this technique to encode slower flows is hampered by diffusion weighting and phase error introduced by gradient hardware imperfections. In this study, a new PC-MRI technique is developed using stimulated echo preparation to overcome these challenges. Flows as slow as 1 μm/s are measured and validated using controlled water flow through a pipe at 4.7 T. The error in measured flow rate obtained by integrating the measured velocity over the cross-sectional area of the pipe is less than 10%. The developed method was also able to capture slow natural convection flows appearing in liquids placed inside a horizontal bore magnet. Monitoring the 4D velocity vector field revealed that the natural convection flows decay exponentially with time. This method could be applied in future to study creeping flows, e.g. in tissue.

Real-Time Insights into Biological Events: In-Cell Processes and Protein-Ligand Interactions

FlowNMR has the aim of continuously monitoring processes that occur in conditions that are not compatible with being carried out within a closed tube. However, it is sample intensive and not suitable for samples, such as proteins or living cells, that are often available in limited volumes and possibly low concentrations. We here propose a dialysis-based modification of a commercial flowNMR setup that allows for recycling the medium while confining the sample (proteins and cells) within the active volume of the tube. This approach is demonstrated in the specific cases of in-cell NMR and protein-based ligand studies.

Practical aspects of real-time pure shift HSQC experiments

Pure shift NMR spectroscopy has become an efficient tool for improving resolution in proton NMR spectra by removing the effect of homonuclear couplings. The introduction of real-time acquisition methods has allowed the main drawback of pure shift NMR, the long experiment times needed, to be circumvented. Real-time methods use periodic application of J-refocusing pulse sequence elements, acquiring a single free induction decay, in contrast to previous methods that construct a pure shift interferogram by concatenating excerpts from multiple free induction decays. In the important heteronuclear single-quantum correlation experiment, implementing real-time pure shift data acquisition typically leads to the simultaneous improvement of both resolution and sensitivity. The current limitations of and problems with real-time pure shift acquisition methods are discussed here in the context of heteronuclear single-quantum correlation experiments. We aim to provide a detailed account of the technical challenges, together with a practical guide to exploiting the full potential of such methods.

Suppression of 13C satellites in 1H DOSY spectra

Diffusion-ordered spectroscopy (DOSY) is a valuable tool for the analysis of intact mixtures, since it can separate the signals of components according to their apparent diffusion coefficients. However, DOSY experiments are acutely sensitive to spectral quality, and especially to signal overlap, which can lead to misleading apparent diffusion coefficients. Here, we introduce a new NMR experiment to reduce signal overlap in mixtures with a wide range of concentrations, by removing one-bond ¹³C satellites. In such high dynamic range mixtures, ¹³C isotopomer signals from major components can overlap with signals from minor components, causing problematic distortions in the diffusion domain of a DOSY spectrum. The new method, Oneshot-iDISPEL, is a combination of the Oneshot and DISPEL experiments, and its performance has been demonstrated on a Greek alcoholic beverage, ouzo, which contains small amounts of anise flavour components and sucrose. Ethanol is a major component, and the suppression of its ¹³C satellites reduces signal overlap with minor components, offering significant improvement in DOSY spectra.

Homonuclear decoupling in the 13 C indirect dimension of HSQC experiments for 13 C-enriched compounds

The two most compelling methods for broadband homonuclear decoupling currently available, Zangger-Sterk (ZS) and pure shift yielded by chirp excitation (PSYCHE), were successfully adapted and tested on the ¹³ C isotope. When applied during the indirect carbon evolution in the HSQC experiment, they both entirely eliminated the extended carbon-carbon multiplet structures observed in this dimension of a non-decoupled HSQC spectrum of ¹³ C-enriched cholesterol. The optimized selective pulse modulated using novel non-equidistant scheme for multisite refocusing (ZS) and the small flip angle saltire chirps (PSYCHE) both proved to be robust and efficient in providing decoupled spectra with a sensitivity of about 25% that of the non-decoupled HSQC spectra with improved quality compared to earlier results.

A macrocyclic receptor containing two viologen species connected by conjugated terphenyl groups

A macrocyclic receptor molecule containing two viologen species connected by conjugated terphenyl groups has been designed and synthesised. The single-crystal X-ray structure shows that the two viologen residues have a transannular NN separation of ca. 7.4 Å. Thus, the internal cavity dimensions are suitable for the inclusion of π-electron-rich species. The macrocycle is redox active, and can accept electrons from suitable donor species including triethylamine, resulting in a dramatic colour change from pale yellow to dark green as a consequence of the formation of a paramagnetic bis(radical cationic) species. Cyclic voltammetry shows that the macrocycle can undergo two sequential and reversible reduction processes (E1/2 = -0.65 and -0.97 V vs. Fc/Fc+). DFT and TD-DFT studies accurately replicate the structure of the tetracationic macrocycle and the electronic absorption spectra of the three major redox states of the system. These calculations also showed that during electrochemical reduction, the unpaired electron density of the radical cations remained relatively localised within the heterocyclic rings. The ability of the macrocycle to form supramolecular complexes was confirmed by the formation of a pseudorotaxane with a guest molecule containing a π-electron-rich 1,5-dihydroxynaphthalene derivative. Threading and dethreading of the pseudorotaxane was fast on the NMR timescale, and the complex exhibited an association constant of 150 M-1 (±30 M-1) as calculated from 1H NMR titration studies.

PSYCHE Pure Shift NMR Spectroscopy

Broadband homodecoupling techniques in NMR, also known as "pure shift" methods, aim to enhance spectral resolution by suppressing the effects of homonuclear coupling interactions to turn multiplet signals into singlets. Such techniques typically work by selecting a subset of "active" nuclear spins to observe, and selectively inverting the remaining, "passive", spins to reverse the effects of coupling. Pure Shift Yielded by Chirp Excitation (PSYCHE) is one such method; it is relatively recent, but has already been successfully implemented in a range of different NMR experiments. Paradoxically, PSYCHE is one of the trickiest of pure shift NMR techniques to understand but one of the easiest to use. Here we offer some insights into theoretical and practical aspects of the method, and into the effects and importance of the experimental parameters. Some recent improvements that enhance the spectral purity of PSYCHE spectra will be presented, and some experimental frameworks, including examples in 1D and 2D NMR spectroscopy, for the implementation of PSYCHE will be introduced.

Improving the Interpretation of Small Molecule Diffusion Coefficients

Diffusion-ordered NMR spectroscopy (DOSY) is increasingly widely used for the analysis of mixtures by NMR spectroscopy, dispersing the signals of different species according to their diffusion coefficients. DOSY is used primarily to distinguish between the signals of different species, with the interpretation of the diffusion coefficients observed usually being purely qualitative, for example to deduce whether one species is bigger or smaller than another. In principle, the actual values of diffusion coefficient obtained carry important information about the sizes of different species and on interactions between species, but the relationship between diffusion coefficient and molecular mass is in general a very complex one. Here a recently proposed analytical relationship between diffusion coefficient and molecular mass for the restricted case of small organic molecules is tested against a wide range of data from the scientific literature and generalized to cover a range of solvents and temperatures.

Time dependence of NMR observables reveals salient differences in the accumulation of early aggregated species between human islet amyloid polypeptide and amyloid-β

Proton NMR shows that IAPP fibril formation does not involve the accumulation of early aggregated species, in contrast with Aβ.

Bipyrrolidine salan alkoxide complexes of lanthanides: synthesis, characterisation, activity in the polymerisation of lactide and mechanistic investigation by DOSY NMR

Dimeric lanthanide alkoxide and hydroxide complexes with salan ligands have been prepared with Nd, Sm and Yb. Monitoring their activity in the polymerisation of lactide by ¹H DOSY NMR reveals a dinuclear catalytic active species.

Effect of convection and B1 inhomogeneity on singlet relaxation experiments

Nuclear spin singlet lifetimes can often exceed the T₁ length scales by a large factor. This property makes them suitable for polarization storage. The measurement of such long lifetimes itself can become challenging due to the influence of even very weak relaxation mechanisms. Here we show that a judicious choice of the singlet-to-triplet conversion method is highly important in order to achieve reliable singlet relaxation measurements. In particular, we identify thermal convection, in connection with B₁ field gradients, asa significant apparent decay mechanism, which limits the ability to measure the true singlet state lifetimes. Highly B₁-compensated broadband singlet excitation/detection sequences are shown to minimize the influence of macroscopic molecular motion and B₁ inhomogeneity.

Combined maximum-quantum and DOSY 3D experiments provide enhanced resolution for small molecules in mixtures

We illustrate here as the combination of high-order maximum-quantum (MaxQ) and Diffusion-Ordered SpectroscopY (DOSY) NMR experiments in a 3D layout allows superior resolution for crowded NMR spectra. Non-uniform sampling (NUS) allows compressing the experimental time effectively to reasonable durations. Because diffusion effects were encoded within multiple-quantum coherences, increased sensitivity to magnetic field gradients is observed, requiring compensation for convection effects. The experiment was demonstrated on the spectra of a mix of small polyaromatic molecules. Specifically, in the case analyzed, the experiment provided an extreme simplification through the MaxQDOSY-MaxQ projection plane that presents one peak per molecule. Copyright © 2016 John Wiley & Sons, Ltd.

Applications of NMR diffusion methods with emphasis on ion pairing in inorganic chemistry: a mini-review

This mini-review provides a brief overview of the use of NMR diffusion methods in connection with estimating molecular weights in solution, recognizing hydrogen bonding and encapsulation processes and, primarily, identifying and estimating the varying degrees of ion pairing. Copyright © 2016 John Wiley & Sons, Ltd.

Selective diffusion spectroscopy using excitation sculpting

Diffusion spectroscopy NMR provides a sensitive and fast way of determining diffusion coefficient. The coefficient is measured by fitting attenuation of resonance intensities to the Stejskal-Tanner equation, but, because it is an exponential equation, this fitting is quite sensitive to experimental artefacts. Intense resonances in NMR spectra, such as solvent signals, are a particular problem because small fractions of intensity of the intense resonances can significantly change the intensities of minor resonances and distort their calculated diffusion coefficients. This problem can be overcome by selective excitation of only the minor resonances, and the method of choice for this is excitation sculpting. This paper shows that the conventional excitation sculpting pulse sequence can be used directly for DOSY spectroscopy with minimal modification. The sequence suppresses intense resonances very effectively, allowing the reproducible measurement of diffusion coefficients of minor solutes in a solvent containing five separate resonances. It is sensitive and robust to convection. Excitation sculpting will allow the application of diffusion spectroscopy to samples which include multiple intense resonances, such as polymeric solvents. Copyright © 2015 John Wiley & Sons, Ltd.

Reconstructing diffusion ordered NMR spectroscopy by simultaneous inversion of Laplace transform

2D diffusion-ordered NMR spectroscopy (DOSY) has been widely recognized as a powerful tool for analyzing mixtures and probing inter-molecular interactions in situ. But it is difficult to differentiate molecules with similar diffusion coefficients in presence of overlapped spectra. Its performance is susceptible to the number of chemical components, and usually gets worse when the number of components increases. Here, to alleviate the problem, numerical simultaneous inversion of Laplace transform (SILT) of many related variables is proposed for reconstructing DOSY spectrum (SILT-DOSY). The advantage of the proposed method in comparison to other methods is that it is capable of estimating the number of analytes more accurately and deriving corresponding component spectra, which in turn leads to the more reliable identification of the components.

Size-exclusion chromatographic NMR under HR-MAS

The addition of stationary phases or sample modifiers can be used to modify the separation achievable in the diffusion domain of diffusion NMR experiments or provide information on the nature of the analyte-sample modifier interaction. Unfortunately, the addition of insoluble chromatographic stationary phases can lead to line broadening and degradation in spectral resolution, largely because of differences in magnetic susceptibility between the sample and the stationary phase. High-resolution magic angle spinning (HR-MAS) techniques can be used to remove this broadening. Here, we attempt the application of HR-MAS to size-exclusion chromatographic NMR with limited success. Observed diffusion coefficients for polymer molecular weight reference standards are shown to be larger than those obtained on static samples. Further investigation reveals that under HR-MAS it is possible to obtain reasonably accurate estimates of diffusion coefficients, using either full rotor synchronisation or sophisticated pulse sequences. The requirement for restricting the sample to the centre of the MAS rotor to ensure homogeneous magnetic and RF fields is also tested. Copyright © 2016 John Wiley & Sons, Ltd.

19 F NMR matrix-assisted DOSY: a versatile tool for differentiating fluorinated species in mixtures

NMR is the most versatile tool for the analysis of organic compounds and, in combination with Diffusion-Ordered Spectroscopy ('DOSY'), can give information on compounds in complex mixtures without the need for physical separation. In mixtures where the components' diffusion coefficients are nearly identical, for example because of similar sizes, Matrix-Assisted DOSY ('MAD') can help separate the signals of different constituents, resolving their spectra. Unfortunately, DOSY (including MAD) typically fails where signals overlap, as is common in ¹ H NMR. Using ¹⁹ F NMR avoids such problems, because the great sensitivity of the ¹⁹ F chemical shift to local environment leads to very well-dispersed spectra. Another advantage is the absence of any ¹⁹ F background signals from the matrices typically used, avoiding interference with the analyte signals. In this study, differentiation among fluorophenol and fluoroaniline isomers was evaluated using normal and reverse micelles-of sodium dodecyl sulfate (SDS), cetyltrimethylammonium bromide (CTAB) and dioctyl sodium sulfosuccinate (AOT)-as matrices. These surfactants provide useful diffusion separation in these difficult mixtures, with all the solutes interacting with the matrices to different extents, in some cases leading to differences in diffusion coefficient of more than 30%. The best matrices for separating the signals of both acid and basic species were shown to be AOT and CTAB, which are useful over a wide range of surfactant concentration. Copyright © 2016 John Wiley & Sons, Ltd.