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.
Highlights
Protein dynamics is intimately tied to biological function
Quantitative analysis of Nonuniform sampling (NUS) spectra has been hampered by the nonlinearity of most techniques used for reconstruction of this type of data.[4−7] nonlinearity of signal intensities has been identified as a major problem in quantifying relaxation rate constants,[7] which are typically evaluated from the decay or build-up of signal intensity
We demonstrate the accordion-NUS method by determining R1 relaxation rate constants and their estimated uncertainties at various sampling densities
Summary
Developments in NMR spectroscopy have made it possible to study protein dynamics in exquisite detail and over a wide range of time scales.[1−3] The challenge today is to achieve accurate measurements under conditions where the experiment time might be severely limited because of stability issues, such as for proteins in living cells, or due to time-dependent phenomena, such as amyloid formation or other types of phase transitions. Nonuniform sampling (NUS) is increasingly used as a timesaving method in NMR spectroscopy.[4] quantitative analysis of NUS spectra has been hampered by the nonlinearity of most techniques used for reconstruction of this type of data.[4−7] nonlinearity of signal intensities has been identified as a major problem in quantifying relaxation rate constants,[7] which are typically evaluated from the decay or build-up of signal intensity. Several studies have addressed this problem, showing that careful consideration of both sampling schemes and data modeling are needed to reach reliable results.[7−9]
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