Sensitivity of Nonuniform Sampling NMR

Abstract

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.

Interpolating and extrapolating with hmsIST: seeking a tmax for optimal sensitivity, resolution and frequency accuracy

“…al. (Palmer MR et al 2015) turns out to be very close to the traditionally measured SNR (SN rms R) of a reconstructed NUS simulated time-equivalent practical implementation (see below). This is not to state that the iSNR and SN rms R are of the same nature as the rationale behind the two concepts is entirely different.…”

“…The non-Gaussian character can be described by calculating the kurtosis value, the fourth standardized statistical moment. In (Palmer MR et al 2015), the group extend the work of (Rovnyak et al 2004), now to include NUS sampling profiles. Both studies calculate iSNR formulae in the time-domain.…”

“…More recently, Rovnyak and coworkers (Palmer MR et al 2015) extended their theoretical analysis to distributing the acquired points according to NUS sampling profiles using a weighted sampling scheme, which needs to see the required implementation procedure. That is, the data point sampled at 1.256 T 2 in an exponential matched sampling is sampled with a weight of 0.2846 of the initial point, not a probability of 0.2846 the initial point.…”

Accurate determination of rates from non-uniformly sampled relaxation data

“…Indeed, there is no general consensus for how far an indirect dimension should be sampled (Hyberts et al 2013) though the signal-to-noise ratio (S/N) is maximized when the indirect dimension is sampled to 1.26*T 2 (Rovnyak et al 2004) and resolution is maximized when the indirect dimension is sampled to 3.14*T 2 . However, recent work has shown that weighted NUS can lead to simultaneous improvements in S/N and resolution beyond 1.26*T 2 (Palmer et al 2015). Sampling to maximize the resolution or sometimes even the S/N can lead to prohibitively long experiment times for serially collected data.…”

NMR of Macromolecular Assemblies and Machines at 1 GHz and Beyond: New Transformative Opportunities for Molecular Structural Biology

“…Rather than discrete Fourier transform, NUS data sets are processed using reconstruction algorithms (68). Non-uniform sampling using random schedules weighted by a decaying function results in bona fide time domain sensitivity enhancements by reducing the number of points acquired, thereby allowing for more transients to be acquired in a given time frame (69–72). NUS can also be used to obtain resolution enhancement by acquiring out to a longer acquisition time without increasing the number of points.…”