Optimising magnetic resonance sampling patterns for parametric characterisation

A Monte Carlo algorithm to improve the measurement efficiency of low-field nuclear magnetic resonance

Nuclear magnetic resonance (NMR) has shown good applications in engineering fields such as well logging and rubber material ageing assessment. However, due to the low magnetic field strength of NMR sensors and the complex working conditions of engineering sites, the signal-to-noise ratio (SNR) of NMR signals is low, and it is usually necessary to increase the number of repeated measurements to improve the SNR, which means a longer measurement time. Therefore, it is especially important to set the measurement parameters appropriately for onsite NMR. In this paper, we propose a stochastic simulation using Monte Carlo methods to predict the measurement curves of [Formula: see text] and [Formula: see text] and correct the measurement parameters of the next step according to the previous measurement results. The method can update the measurement parameters in real time and perform automatic measurements. At the same time, this method greatly reduces the measurement time. The experimental results show that the method is suitable for the measurement of the self-diffusion coefficient D0 and longitudinal relaxation time T1, which are frequently used in NMR measurements.

Optimal design of adaptively sampled NMR experiments for measurement of methyl group dynamics with application to a ribosome-nascent chain complex

NMR measurements of cross-correlated nuclear spin relaxation provide powerful probes of polypeptide dynamics and rotational diffusion, free from contributions due to chemical exchange or interactions with external spins. Here, we report on the development of a sensitivity-optimized pulse sequence for the analysis of the differential relaxation of transitions within isolated ¹³CH₃ spin systems, in order to characterise rotational diffusion and side chain order through the product S²τ_c. We describe the application of optimal design theory to implement a real-time 'on-the-fly' adaptive sampling scheme that maximizes the accuracy of the measured parameters. The increase in sensitivity obtained using this approach enables quantitative measurements of rotational diffusion within folded states of translationally-arrested ribosome-nascent chain complexes of the FLN5 filamin domain, and can be used to place strong limits on interactions between the domain and the ribosome surface.

Rapid NMR Relaxation Measurements Using Optimal Nonuniform Sampling of Multidimensional Accordion Data Analyzed by a Sparse Reconstruction Method

Nonuniform sampling (NUS) of multidimensional NMR data offers significant time savings while improving spectral resolution or increasing sensitivity per unit time. However, NUS has not been widely used for quantitative analysis because of the nonlinearity of most methods used to model NUS data, which leads to problems in estimating signal intensities, relaxation rate constants, and their error bounds. Here, we present an approach that avoids these limitations by combining accordion spectroscopy and NUS in the indirect dimensions of multidimensional spectra and then applying sparse exponential mode analysis, which is well suited for analyzing accordion-type relaxation data in a NUS context. By evaluating the Cramér-Rao lower bound of the variances of the estimated relaxation rate constants, we achieve a robust benchmark for the underlying reconstruction model. Furthermore, we design NUS schemes optimized with respect to the information theoretical lower bound of the error in the parameters of interest, given a specified number of sampling points. The accordion-NUS method compares favorably with conventional relaxation experiments in that it produces identical results, within error, while shortening the length of the experiment by an order of magnitude. Thus, our approach enables rapid acquisition of NMR relaxation data for optimized use of spectrometer time or accurate measurements on samples of limited lifetime.

Optimising sampling patterns for bi-exponentially decaying signals

A recently reported method, based on the Cramér-Rao Lower Bound theory, for optimising sampling patterns for a wide range of nuclear magnetic resonance (NMR) experiments is applied to the problem of optimising sampling patterns for bi-exponentially decaying signals. Sampling patterns are optimised by minimizing the percentage error in estimating the most difficult to estimate parameter of the bi-exponential model, termed the objective function. The predictions of the method are demonstrated in application to pulsed field gradient NMR data recorded for the two-component diffusion of a binary mixture of methane/ethane in a zeolite. It is shown that the proposed method identifies an optimal sampling pattern with the predicted objective function being within 10% of that calculated from the experiment dataset. The method is used to advise on the number of sampled points and the noise level needed to resolve two-component systems characterised by a range of ratios of populations and diffusion coefficients. It is subsequently illustrated how the method can be used to reduce the experiment acquisition time while still being able to resolve a given two-component system.