Time-domain signal modelling in multidimensional NMR experiments for estimation of relaxation parameters

Extreme Nonuniform Sampling for Protein NMR Dynamics Studies in Minimal Time

NMR spectroscopy is an extraordinarily rich source of quantitative dynamics of proteins in solution using spin relaxation or chemical exchange saturation transfer (CEST) experiments. However, ¹⁵N-CEST measurements require prolonged multidimensional, so-called pseudo-3D HSQC experiments where the pseudo dimension is a radio frequency offset Δω of a weak ¹⁵N saturation field. Nonuniform sampling (NUS) approaches have the potential to significantly speed up these measurements, but they also carry the risk of introducing serious artifacts and the systematic optimization of nonuniform sampling schedules has remained elusive. It is demonstrated here how this challenge can be addressed by using fitted cross-peaks of a reference 2D HSQC experiment as footprints, which are subsequently used to reconstruct cross-peak amplitudes of a pseudo-3D data set as a function of Δω by a linear least-squares fit. It is shown for protein Im7 how the approach can yield highly accurate CEST profiles based on an absolutely minimally sampled (AMS) data set allowing a speed-up of a factor 20-30. Spectrum-specific optimized nonuniform sampling (SONUS) schemes based on the Cramer-Rao lower bound metric were critical to achieve such a performance, revealing also more general properties of optimal sampling schedules. This is the first systematic exploration and optimization of NUS schedules for the dramatic speed-up of quantitative multidimensional NMR measurements that minimize unwanted errors.