Rapid measurement of heteronuclear transverse relaxation rates using non-uniformly sampled R1 ρ accordion experiments

Sven Wernersson; Göran Carlström; Andreas Jakobsson; Mikael Akke

doi:10.5194/mr-2-571-2021

Rapid measurement of heteronuclear transverse relaxation rates using non-uniformly sampled R_{1 ρ} accordion experiments

Magn Reson (Gott). 2021 Jul 12;2(2):571-587. doi: 10.5194/mr-2-571-2021. eCollection 2021.

Authors

Sven Wernersson¹, Göran Carlström², Andreas Jakobsson³, Mikael Akke¹

Affiliations

¹ Biophysical Chemistry, Center for Molecular Protein Science, Department of Chemistry, Lund University, P.O. Box 124, 22100 Lund, Sweden.
² Centre for Analysis and Synthesis, Department of Chemistry, Lund University, P.O. Box 124, 22100 Lund, Sweden.
³ Department of Mathematical Statistics, Lund University, P.O. Box 118, 22100 Lund, Sweden.

Abstract

Multidimensional, heteronuclear NMR relaxation methods are used extensively to characterize the dynamics of biological macromolecules. Acquisition of relaxation datasets on proteins typically requires significant measurement time, often several days. Accordion spectroscopy offers a powerful means to shorten relaxation rate measurements by encoding the "relaxation dimension" into the indirect evolution period in multidimensional experiments. Time savings can also be achieved by non-uniform sampling (NUS) of multidimensional NMR data, which is used increasingly to improve spectral resolution or increase sensitivity per unit time. However, NUS is not commonly implemented in relaxation experiments, because most reconstruction algorithms are inherently nonlinear, leading to problems when estimating signal intensities, relaxation rate constants and their error bounds. We have previously shown how to avoid these shortcomings by combining accordion spectroscopy with NUS, followed by data reconstruction using sparse exponential mode analysis, thereby achieving a dramatic decrease in the total length of longitudinal relaxation experiments. Here, we present the corresponding transverse relaxation experiment, taking into account the special considerations required for its successful implementation in the framework of the accordion-NUS approach. We attain the highest possible precision in the relaxation rate constants by optimizing the NUS scheme with respect to the Cramér-Rao lower bound of the variance of the estimated parameter, given the total number of sampling points and the spectrum-specific signal characteristics. The resulting accordion-NUS $R_{1 ρ}$ relaxation experiment achieves comparable precision in the parameter estimates compared to conventional CPMG (Carr-Purcell-Meiboom-Gill) $R_{2}$ or spin-lock $R_{1 ρ}$ experiments while saving an order of magnitude in experiment time.