Ultrafast methods for relaxation and diffusion

Ultrafast T1-T1ρ NMR for Correlating Different Motional Regimes of Molecules

Nuclear magnetic resonance (NMR) relaxation times provide detailed information about molecular motions and local chemical environments. Longitudinal T1 relaxation time is most often sensitive to relatively fast, nano- to picosecond ranges of molecular motion. Rotating frame T1ρ relaxation time reflects a much slower, micro- to millisecond range of motion, and the motional regime can be tuned by changing spin-lock field strength. Conventional methods for measuring T1 and T1ρ relaxation times are time-consuming, since experiments must be repeated many times with incremented magnetization recovery or decay delay. In this work, we introduce two novel and efficient NMR methods to correlate the T1 and T1ρ relaxation times. The first method, IR-SPICY, combines the conventional T1 inversion recovery (IR) with the single-scan T1ρ detection-based spin-lock cycle (SPICY). The second method, ultrafast (UF) IR-SPICY, allows measurement of whole two-dimensional T1-T1ρ correlation data in a single scan, in a couple of seconds, based on spatial encoding of the T1 dimension. We demonstrate the performance of the methods by studying relaxation of water in porous silica and hydrogel samples, latter acting as a model of the articular cartilage extracellular matrix. The methods allow correlating different molecular motional regimes, potentially providing unprecedented information about various chemical and biochemical systems, such as structures and fluid dynamics in porous materials, macromolecular changes in tissues, and protein dynamics. One to three orders of magnitude shortened experiment time enable the studies of changing or degrading samples. Furthermore, the single-scan approach may significantly facilitate the use of modern nuclear-spin hyperpolarization techniques to enhance the sensitivity of T1-T1ρ measurements by several orders of magnitude.

Ultrafast Nuclear Magnetic Resonance as a Tool to Detect Rapid Chemical Change in Solution

Ultrafast nuclear magnetic resonance (NMR) uses spatial encoding to record an entire two-dimensional data set in just a single scan. The approach can be applied to either Fourier-transform or Laplace-transform NMR. In both cases, acquisition times are significantly shorter than traditional 2D/Laplace NMR experiments, which allows them to be used to monitor rapid chemical transformations. This Perspective outlines the principles of ultrafast NMR and focuses on examples of its use to detect fast molecular conversions in situ with high temporal resolution. We discuss how this valuable tool can be applied in the future to study a much wider variety of novel reactivity.

Fast Pure Shift NMR Spectroscopy Using Attention-Assisted Deep Neural Network

Pure shift NMR spectroscopy enables the robust probing on molecular structure and dynamics, benefiting from great resolution enhancements. Despite extensive application landscapes in various branches of chemistry, the long experimental times induced by the additional time dimension generally hinder its further developments and practical deployments, especially for multi-dimensional pure shift NMR. Herein, this study proposes and implements the fast, reliable, and robust reconstruction for accelerated pure shift NMR spectroscopy with lightweight attention-assisted deep neural network. This deep learning protocol allows one to regain high-resolution signals and suppress undersampling artifacts, as well as furnish high-fidelity signal intensities along with the accelerated pure shift acquisition, benefitting from the introduction of the attention mechanism to highlight the spectral feature and information of interest. Extensive results of simulated and experimental NMR data demonstrate that this attention-assisted deep learning protocol enables the effective recovery of weak signals that are almost drown in the serious undersampling artifacts, and the distinction and recognition of close chemical shifts even though using merely 5.4% data, highlighting its huge potentials on fast pure shift NMR spectroscopy. As a result, this study affords a promising paradigm for the AI-assisted NMR protocols toward broader applications in chemistry, biology, materials, and life sciences, and among others.

CAT on MOUSE: Control and automation of temperature for single-sided NMR instruments such as NMR-MOUSE

Temperature-dependent experiments are a rapidly growing area of interest for low-field NMR. In this work, we present a new device for wide-range temperature control for single-sided NMR instruments. The presented device, called CAT, is simple to build, inexpensive, and easy to modify to accommodate different samples. We present the capabilities of the device using a freezing temperature study of acetic acid/water mixtures. Additionally, we present the stability of the device over long measurement times. We believe that by introducing such a device with an open-source design, we allow researchers to use it in a wide range of applications and to fully incorporate variable-temperature studies in the world of single-sided instruments.

SHARPER-DOSY: Sensitivity enhanced diffusion-ordered NMR spectroscopy

Since its discovery in mid-20^th century, the sensitivity of Nuclear Magnetic Resonance (NMR) has increased steadily, in part due to the design of new, sophisticated NMR experiments. Here we report on a liquid-state NMR methodology that significantly increases the sensitivity of diffusion coefficient measurements of pure compounds, allowing to estimate their sizes using a much reduced amount of material. In this method, the diffusion coefficients are being measured by analysing narrow and intense singlets, which are invariant to magnetic field inhomogeneities. The singlets are obtained through signal acquisition embedded in short (<0.5 ms) spin-echo intervals separated by non-selective 180° or 90° pulses, suppressing the chemical shift evolution of resonances and their splitting due to J couplings. The achieved 10-100 sensitivity enhancement results in a 100-10000-fold time saving. Using high field cryoprobe NMR spectrometers, this makes it possible to measure a diffusion coefficient of a medium-size organic molecule in a matter of minutes with as little as a few hundred nanograms of material.

Quantitative stray-field T1 relaxometry with the matrix pencil method

The matrix pencil method (MPM) is tested as an approach to quantitatively process multiexponential low-field nuclear magnetic resonance T₁ relaxometry data. The data is obtained by measuring T₁ saturation recovery curves in the highly inhomogeneous magnetic field of a stray-field sensor. 0.9% brine solutions, doped with different concentrations of a Gd³⁺ containing contrast agent, serve as test liquids. Relaxation-times as a function of contrast-agent concentration along with the T₁ relaxation curves for combinations of multiple different test liquids are measured, and the results from processing using MPM as well as inverse Laplace transformation as a benchmark are compared. The relaxation-time resolution limits of both procedures are probed by gradually reducing the difference between the relaxation-times of two liquids measured simultaneously. The sensitivity to quantify the relative contribution of each component to the magnetization build-up curve is explored by changing their volume ratio. Furthermore, the potential to resolve systems with more than two components is tested. For the systems under test, MPM shows superior performance in separating two or three relaxation components, respectively and effectively quantifying the time constants.

SPICY: a method for single scan rotating frame relaxometry

T _1ρ is an NMR relaxation mode that is sensitive to low frequency molecular motions, making it an especially valuable tool in biomolecular research. Here, we introduce a new method, SPICY, for measuring T_1ρ relaxation times. In contrast to conventional T_1ρ experiments, in which the sequence is repeated many times to determine the T_1ρ time, the SPICY sequence allows determination of T_1ρ within a single scan, shortening the experiment time remarkably. We demonstrate the method using ¹H T_1ρ relaxation dispersion experiments. Additionally, we combine the sequence with spatial encoding to produce 1D images in a single scan. We show that T_1ρ relaxation times obtained using the single scan approach are in good agreement with those obtained using the traditional experiments.

A new perspective of molecular diffusion by nuclear magnetic resonance

The diffusion-weighted NMR signal acquired using Pulse Field Gradient (PFG) techniques, allows for extrapolating microstructural information from porous materials and biological tissues. In recent years there has been a multiplication of diffusion models expressed by parametric functions to fit the experimental data. However, clear-cut criteria for the model selection are lacking. In this paper, we develop a theoretical framework for the interpretation of NMR attenuation signals in the case of Gaussian systems with stationary increments. The full expression of the Stejskal-Tanner formula for normal diffusing systems is devised, together with its extension to the domain of anomalous diffusion. The range of applicability of the relevant parametric functions to fit the PFG data can be fully determined by means of appropriate checks to ascertain the correctness of the fit. Furthermore, the exact expression for diffusion weighted NMR signals pertaining to Brownian yet non-Gaussian processes is also derived, accompanied by the proper check to establish its contextual relevance. The analysis provided is particularly useful in the context of medical MRI and clinical practise where the hardware limitations do not allow the use of narrow pulse gradients.

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.

Deeper Insight into Photopolymerization: The Synergy of Time-Resolved Nonuniform Sampling and Diffusion NMR

The comprehensive real-time in situ monitoring of chemical processes is a crucial requirement for the in-depth understanding of these processes. This monitoring facilitates an efficient design of chemicals and materials with the precise properties that are desired. This work presents the simultaneous utilization and synergy of two novel time-resolved NMR methods, i.e., time-resolved diffusion NMR and time-resolved nonuniform sampling. The first method allows the average diffusion coefficient of the products to be followed, while the second method enables the particular products to be monitored. Additionally, the average mass of the system is calculated with excellent resolution using both techniques. Employing both methods at the same time and comparing their results leads to the unequivocal validation of the assignment in the second method. Importantly, such validation is possible only via the simultaneous combination of both approaches. While the presented methodology was utilized for photopolymerization, it can also be employed for any other polymerization process, complexation, or, in general, chemical reactions in which the evolution of mass in time is of importance.

Sensitive, Efficient and Portable Analysis of Molecular Exchange Processes by Hyperpolarized Ultrafast NMR

Molecular exchange processes are ubiquitous in nature. Here, we introduce a method to analyze exchange processes by using low-cost, portable, single-sided NMR instruments. The inherent magnetic field inhomogeneity of the single-sided instruments is exploited to achieve diffusion contrast of exchange sites and spatial encoding of 2D data. This so-called ultrafast diffusion exchange spectroscopy method shortens the experiment time by two to four orders of magnitude. Furthermore, because full 2D data are measured in a single scan (in a fraction of a second), the sensitivity of the experiment can be improved by several orders of magnitude using so-called nuclear spin hyperpolarization methods (in this case, dissolution dynamic nuclear polarization). As the first demonstration of the feasibility of the method in various applications, we show that the method enables quantification of intra- and extracellular exchange of water in a yeast cell suspension.

Exact Solutions of the Bloch Equations of a Two-Level Atom Driven by the Generalized Double Exponential Quotient Pulses with Dephasing

We theoretically investigate a two-level atom driven by a time-dependent external field with a generalized double exponential temporal shape, in the presence of dephasing. Therefore, we provide exact analytical solutions for the population inversion, the real and the imaginary parts of the coherence for a family of chirped and time-dependent laser waveforms. We demonstrate that the remaining atomic population inversion can be controlled by the manipulation of the pulse’s shape structure.

Ultrafast 2D NMR for the analysis of complex mixtures

2D NMR is extensively used in many different fields, and its potential for the study of complex biochemical or chemical mixtures has been widely demonstrated. 2D NMR gives the ability to resolve peaks that overlap in 1D spectra, while providing both structural and quantitative information. However, complex mixtures are often analysed in situations where the data acquisition time is a crucial limitation, due to an ongoing chemical reaction or a moving sample from a hyphenated technique, or to the high-throughput requirement associated with large sample collections. Among the great diversity of available fast 2D methods, ultrafast (or single-scan) 2D NMR is probably the most general and versatile approach for complex mixture analysis. Indeed, ultrafast NMR has undergone an impressive number of methodological developments that have helped turn it into an efficient analytical tool, and numerous applications to the analysis of mixtures have been reported. This review first summarizes the main concepts, features and practical limitations of ultrafast 2D NMR, as well as the methodological developments that improved its analytical potential. Then, a detailed description of the main applications of ultrafast 2D NMR to mixture analysis is given. The two major application fields of ultrafast 2D NMR are first covered, i.e., reaction/process monitoring and metabolomics. Then, the potential of ultrafast 2D NMR for the analysis of hyperpolarized mixtures is described, as well as recent developments in oriented media. This review focuses on high-resolution liquid-state 2D experiments (including benchtop NMR) that include at least one spectroscopic dimension (i.e., 2D spectroscopy and DOSY) but does not cover in depth applications without spectral resolution and/or in inhomogeneous fields.