We report dramatic sensitivity enhancements in multidimensional MAS NMR spectra by the use of nonuniform sampling (NUS) and introduce Maximum Entropy Interpolation (MINT) processing that assures the linearity between the time- and frequency domains of the NUS acquired datasets. A systematic analysis of sensitivity and resolution in 2D and 3D NUS spectra reveals that with NUS at least one-and-a-half to two-fold sensitivity enhancement can be attained in each indirect dimension without compromising the spectral resolution. These enhancements are similar to or higher than those attained by the newest-generation commercial cryogenic probes. We explore the benefits of this NUS/MaxEnt approach in proteins and protein assemblies using 1-73-(U-13C,15N)/74-108-(U-15N) E. coli thioredoxin reassembly. We demonstrate that in thioredoxin reassembly, NUS permits acquisition of high-quality 3D-NCACX spectra, which are inaccessible with conventional sampling due to prohibitively long experiment times. Of critical importance, issues which hinder NUS-based SNR enhancement in 3D-NMR of liquids are mitigated in the study of solid samples where theoretical enhancements on the order of 3-4 fold are accessible by compounding the NUS-based SNR enhancement of each indirect dimension. NUS/MINT is anticipated to be widely applicable and advantageous for multidimensional heteronuclear MAS NMR spectroscopy of proteins, protein assemblies, and other biological systems.

Many information rich multi-dimensional experiments in nuclear magnetic resonance spectroscopy can benefit from a signal-to-noise ratio (SNR) enhancement up to about two-fold if a decaying signal in an indirect dimension is sampled with nonconsecutive increments, termed non-uniform sampling (NUS). This work provides formal theoretical results and applications to resolve major questions on the scope of the NUS enhancement. First, we introduce the NUS Sensitivity Theorem, that any decreasing sampling density applied to any exponentially decaying signal always results in higher sensitivity (SNR per square root of measurement time) than uniform sampling (US). Several cases will illustrate this theorem, and show that even conservative applications of NUS improve sensitivity by useful amounts. Next, we turn to a serious limitation of uniform sampling: the SNR by US decreases for extending evolution times, and thus total experimental times, beyond 1.26 T2 (T2 = signal decay constant). Thus SNR and resolution cannot be simultaneously improved by extending US beyond 1.26 T2. We find that NUS can eliminate this constraint, and introduce the Matched NUS SNR Theorem: an exponential sampling density matched to the signal decay always improves the SNR with additional evolution time. Though proved for a specific case, broader classes of NUS densities also improve SNR with evolution time. Applications of these theoretical results are given for a soluble plant natural product and a solid tripeptide (u-13C,15N-MLF). These formal results clearly demonstrate the inadequacies of applying US to decaying signals in indirect nD-NMR dimensions, supporting broader adoption of NUS.

Non-uniform sampling (NUS) has been established as a route to obtaining true sensitivity enhancements when recording indirect dimensions of decaying signals in the same total experimental time as traditional uniform incrementation of the indirect evolution period. Theory and experiments have shown that NUS can yield up to two-fold improvements in the intrinsic signal-to-noise ratio (SNR) of each dimension, while even conservative protocols can yield 20–40 % improvements in the intrinsic SNR of NMR data. Applications of biological NMR that can benefit from these improvements are emerging, and in this work we develop some practical aspects of applying NUS nD-NMR to studies that approach the traditional detection limit of nD-NMR spectroscopy. Conditions for obtaining high NUS sensitivity enhancements are considered here in the context of enabling 1H,15N-HSQC experiments on natural abundance protein samples and 1H,13C-HMBC experiments on a challenging natural product. Through systematic studies we arrive at more precise guidelines to contrast sensitivity enhancements with reduced line shape constraints, and report an alternative sampling density based on a quarter-wave sinusoidal distribution that returns the highest fidelity we have seen to date in line shapes obtained by maximum entropy processing of non-uniformly sampled data.

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