Nonlinear sampling in ultrafast Laplace NMR

Automated component analysis in DOSY NMR using information criteria

This study introduces a model selection technique based on Bayesian information criteria for estimating the number of components in a mixture during Diffusion-Ordered Spectroscopy (DOSY) Nuclear Magnetic Resonance (NMR) data analysis. As the accuracy of this technique is dependent on the efficiency of parameter estimators, we further investigate the performance of the Weighted Least Squares (WLS) and Maximum a Posteriori (MAP) estimators. The WLS method, enhanced with meticulously tuned L2-regularization, effectively detects components when the difference in self-diffusion coefficients is more than two-fold, especially when the component with the smaller coefficient has a larger weight ratio. The MAP method, strengthened by a substantial database of prior information, exhibits outstanding precision, decreasing this threshold to 1.5 times. Both estimators provide weight ratio estimates with standard deviations of approximately around 1 percentage point, although the MAP method tends to overestimate the component with a larger self-diffusion coefficient. Deviations from the expected values can exceed 10 percentage points, often due to inaccuracies in component detection. The error estimates are determined using data resampling techniques derived from a large-scale 1000-point experiment and an additional five measurements from a single-component mixture. This approach allowed us to thoroughly examine data distribution characteristics, thereby laying a robust groundwork for future refinement efforts.

Ultrafast transverse relaxation exchange NMR spectroscopy

Molecular exchange between different physical or chemical environments occurs due to either diffusion or chemical transformation. Nuclear magnetic resonance (NMR) spectroscopy provides a means of understanding the molecular exchange in a noninvasive way and without tracers. Here, we introduce a novel two dimensional, single-scan ultrafast Laplace NMR (UF LNMR) method to monitor molecular exchange using transverse relaxation as a contrast. The UF T₂–T₂ relaxation exchange spectroscopy (REXSY) method shortens the experiment time by one to two orders of magnitude compared to its conventional counterpart. Contrary to the conventional EXSY, the exchanging sites are distinguished based on T₂ relaxation times instead of chemical shifts, making the method especially useful for systems including physical exchange of molecules. Therefore, the UF REXSY method offers an efficient means for quantification of exchange processes in various fields such as cellular metabolism and ion transport in electrolytes. As a proof of principle, we studied a halogen-free orthoborate based ionic liquid system and followed molecular exchange between molecular aggregates and free molecules. The results are in good agreement with the conventional exchange studies. Due to the single-scan nature, the method potentially significantly facilitates the use of modern hyperpolarization techniques to boost the sensitivity by several orders of magnitude.

An ultrafast two-dimensional NMR method allows quantification of molecular exchange rates efficiently based on T₂ relaxation contrast.

Quadratic spacing of the effective gradient area for spatially encoded diffusion NMR

Diffusion NMR experiments rely on the measurement of signal attenuation as a function of the area of diffusion-encoding pulsed magnetic-field gradients. In conventional experiments, arbitrary series of gradient values can be used, and different gradient spacing strategies have different advantages. Ultrafast diffusion NMR relies on the spatial parallelisation of effective gradient area values to collect full 2D diffusion data sets in a single scan. Until recently, only linear spacing was available. We have shown that quadratic spacing can be achieved using a tailored frequency swept pulse. Here we describe the design of the pulse and validate it with numerical spin simulations, that make it possible to check the effect of the quadratic spacing pulse at different stages of the pulse sequence. We also show that quadratic spacing makes it possible to use a recently reported analysis method for diffusion NMR, the Matrix Pencil Method. We describe the results obtained with the MPM and those obtained with the direct exponential curve resolution algorithm (DECRA), which also requires quadratic gradient spacing. Overall, these developments open new opportunities for applications of spatially encoded diffusion experiments, such as ultrafast DOSY NMR and ultrafast Laplace NMR.

Ultrafast methods for relaxation and diffusion

Relaxation and diffusion NMR measurements offer an approach to studying rotational and translational motion of molecules non-invasively, and they also provide chemical resolution complementary to NMR spectra. Multidimensional experiments enable the correlation of relaxation and diffusion parameters as well as the observation of molecular exchange phenomena through relaxation or diffusion contrast. This review describes how to accelerate multidimensional relaxation and diffusion measurements significantly through spatial encoding. This so-called ultrafast Laplace NMR approach shortens the experiment time to a fraction and makes even single-scan experiments possible. Single-scan experiments, in turn, significantly facilitate the use of nuclear spin hyperpolarization methods to boost sensitivity. The ultrafast Laplace NMR method is also applicable with low-field, mobile NMR instruments, and it can be exploited in many disciplines. For example, it has been used in studies of the dynamics of fluids in porous materials, identification of intra- and extracellular metabolites in cancer cells, and elucidation of aggregation phenomena in atmospheric surfactant solutions.

Ultrafast Laplace NMR to study metal-ligand interactions in reversible polarisation transfer from parahydrogen

Laplace Nuclear Magnetic Resonance (NMR) can determine relaxation parameters and diffusion constants, giving valuable information about molecular structure and dynamics. Information about relaxation times (T1 and T2) and the self-diffusion coefficient (D) can be extracted from exponentially decaying NMR signals by performing a Laplace transform, which is a different approach to traditional NMR involving Fourier transform of a free induction decay. Ultrafast Laplace NMR uses spatial encoding to collect the entire data set in just a single scan which provides orders of magnitude time savings. In this work we use ultrafast Laplace NMR D-T2 correlation sequences to measure key relaxation (T2) and diffusion (D) parameters of methanolic solutions containing pyridine. For the first time we combine this technique with the hyperpolarisation technique Signal Amplification By Reversible Exchange (SABRE), which employs an iridium catalyst to reversibly transfer polarisation from parahydrogen, to boost the 1H NMR signals of pyridine by up to 300-fold. We demonstrate use of ultrafast Laplace NMR to monitor changes in pyridine T2 and D associated with ligation to the iridium SABRE catalyst and kinetic isotope exchange reactions. The combined 1440-fold reduction in experiment time and 300-fold 1H NMR signal enhancement allow the determination of pyridine D coefficients and T2 values at 25 mM concentrations in just 3 seconds using SABRE hyperpolarised ultrafast Laplace NMR.

Ultrafast diffusion-based unmixing of 1H NMR spectra

We show that the NMR spectra of components in a mixture can be separated using 2D data acquired in less than one second, and an algorithm that is executed in just a few seconds. This NMR unmixing method is based on spatial encoding of the translational diffusion coefficients of the mixture's components, with multivariate processing of the data. This requires a new frequency swept pulse, which is designed and implemented to obtain quadratic spacing of the spatially parallelised gradient dimension. Ultrafast NMR unmixing may help in the analysis of mixtures that evolve in time.

-Frequency-swept pulses for ultrafast spatially encoded NMR

Ultrafast NMR based on spatial encoding yields arbitrary multidimensional spectra in a single scan. The dramatic acceleration afforded by spatial parallelisation makes it possible to capture transient species and processes, and has notably been applied to the monitoring of reactions and the analysis of hyperpolarised species. At the heart of ultrafast NMR lies the spatially sequential manipulation of nuclear spins. This is virtually always achieved by combining a swept radio-frequency pulse with a magnetic field gradient pulse. The dynamics of nuclear spins during these pulse sequence elements is key to understand and design ultrafast NMR experiments, and can often be described by surprisingly simple models. This article describes the spatial encoding of relaxation, chemical shift and diffusion in a common framework and discusses directions for future developments.