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

Abstract

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.

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

“…An early application to protein NMR spectroscopy was the optimal selection of time points for relaxation measurements (40), while applications of the CRLB to parametric estimation of multidimensional NMR spectra, and the evaluation of non-uniform sampling schemes, was reported a few years later (41). More recently, this approach has been applied to droplet size estimation using diffusion NMR experiments (42), and to the optimal parametric estimation of protein relaxation rates in a non-uniformly sampled accordion NMR experiment (43).…”

Software for reconstruction of nonuniformly sampled NMR data

“…[22][23][24][25] Recently, NUS has been combined with accordion spectroscopy where the signals in the indirect dimension of a two-dimensional (2D) NMR spectrum are modulated with the relaxation parameter of interest and may be extracted by measuring only two sparsely sampled 2D spectra. 26 Despite the many advantages of NUS, according to Web of Science, the key publications 6,7,[27][28][29] for the five software packages for NUS processing (MddNMR, hmsIST, Cambridge CS, NESTA-NMR, and SMILE), which we consider in this review, have together in total been cited 68 and 78 times per year in 2018 and 2019 compared with more than 600 annual citations of the popular nmrPipe 30 software package for traditional data processing of multidimensional NMR data. These citation rates suggest that a lot of NMR data that could be recorded with NUS without compromising data quality are recorded with traditional full sampling of the Nyquist grid.…”

“…Such analyses result in highly accurate intensities 22–25 . Recently, NUS has been combined with accordion spectroscopy where the signals in the indirect dimension of a two‐dimensional (2D) NMR spectrum are modulated with the relaxation parameter of interest and may be extracted by measuring only two sparsely sampled 2D spectra 26 …”

Rapid measurement of heteronuclear transverse relaxation rates using non-uniformly sampled R<sub>1ρ</sub> accordion experiments

“…However, most spectral reconstruction algorithms suffer from nonlinearity of signal intensities, which limits 'plug-and-play' use of NUS in quantitative experiments, and requires careful consideration of both sampling schemes and data modeling to produce consistent results and reliable error estimates (Linnet and Teilum, 2016;Mayzel et al, 2017;Stetz and Wand, 2016;Urbańczyk et al, 2017). We recently introduced an approach that avoids these problems by combining accordion spectroscopy with NUS (Carlström et al, 2019), and analyzing the resulting data using DSURE (damped super-resolution estimator), a sparse reconstruction technique enabling maximum-likelihood estimation of the time-domain signal parameters from NUS data (Juhlin et al, 2018;Swärd et al, 2016). We stress the point that accordion spectroscopy encodes the desired relaxation rate constants in the interferogram of the multidimensional data set, and hence the analysis does not rely on measuring intensities in multiple NUS datasets.…”

“…Compared to a conventional relaxation experiment, accordion reduces the experiment time by a factor of M/2, where M is the number of datasets included in the conventional approach, and NUS reduces the experiment time by a factor of Nfull/N, where Nfull is the number of data points sampled in the indirect dimension of the conventional experiment and N is the number of points in the NUS scheme. We previously demonstrated this approach by measuring longitudinal relaxation rate constants (R1) in proteins with time savings of up to a factor of 20 (Carlström et al, 2019). For example, using this approach we have successfully measured R1 on protein samples with 10-fold lower concentration than normally used (Verteramo et al, 2021).…”