title: Sensitivity of nonuniform sampling NMR.
abstract: Many information-rich multidimensional experiments in nuclear magnetic resonance spectroscopy can benefit from a signal-to-noise ratio (SNR) enhancement of up to about 2-fold if a decaying signal in an indirect dimension is sampled with nonconsecutive increments, termed nonuniform sampling (NUS). This work provides formal theoretical results and applications to resolve major questions about the scope of the NUS enhancement. First, we introduce the NUS Sensitivity Theorem in which 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 1.26T2 (T2 = signal decay constant). Thus, SNR and resolution cannot be simultaneously improved by extending US beyond 1.26T2. We find that NUS can eliminate this constraint, and we 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-(13)C,(15)N-MLF). These formal results clearly demonstrate the inadequacies of applying US to decaying signals in indirect nD-NMR dimensions, supporting a broader adoption of NUS.
authors.affiliation: †Department of Chemistry, Bucknell University, Lewisburg, Pennsylvania 17837, United States.
authors.forename: Melissa R
authors.initials: MR
authors.lastname: Palmer
authors.affiliation: ‡Department of Chemistry and Biochemistry, University of Delaware, Newark, Delaware 19716, United States.
authors.forename: Christopher L
authors.initials: CL
authors.lastname: Suiter
authors.affiliation: §Department of Chemistry, Susquehanna University, Selinsgrove, Pennsylvania 17837, United States.
authors.forename: Geneive E
authors.initials: GE
authors.lastname: Henry
authors.affiliation: ∥Department of Mathematics, University of Virginia, Charlottesville, Virginia 22904, United States.
authors.forename: James
authors.initials: J
authors.lastname: Rovnyak
authors.affiliation: ⊥Department of Molecular Biology and Biophysics, University of Connecticut Health Center, Farmington, Connecticut 06030, United States.
authors.forename: Jeffrey C
authors.initials: JC
authors.lastname: Hoch
authors.affiliation: ‡Department of Chemistry and Biochemistry, University of Delaware, Newark, Delaware 19716, United States.
authors.forename: Tatyana
authors.initials: T
authors.lastname: Polenova
authors.affiliation: †Department of Chemistry, Bucknell University, Lewisburg, Pennsylvania 17837, United States.
authors.forename: David
authors.initials: D
authors.lastname: Rovnyak
mesh_terms: D009682:Magnetic Resonance Spectroscopy / Q000379:methods*; D059629:Signal-To-Noise Ratio; D013223:Statistics as Topic