Z -matrix formalism for quantitative noise assessment of covariance nuclear magnetic resonance spectra

Abstract

Due to the limited sensitivity of many nuclear magnetic resonance ͑NMR͒ applications, careful consideration must be given to the effect of NMR data processing on spectral noise. This work presents analytical relationships as well as simulated and experimental results characterizing the propagation of noise by unsymmetric covariance NMR processing, which concatenates two NMR spectra along a common dimension, resulting in a new spectrum showing spin correlations as cross peaks that are not directly measured in either of the two input spectra. It is shown how the unsymmetric covariance spectrum possesses an inhomogeneous noise distribution across the spectrum with the least amount of noise in regions whose rows and columns do not contain any cross or diagonal peaks and with the largest amount of noise on top of signal peaks. Therefore, methods of noise estimation commonly used in Fourier transform spectroscopy underestimate the amount of uncertainty in unsymmetric covariance spectra. Different data processing procedures, including the Z-matrix formalism, thresholding, and maxima ratio scaling, are described to assess noise contributions and to reduce noise inhomogeneity. In particular, determination of a Z score, which measures the difference in standard deviations of a statistic from its mean, for each spectral point yields a Z matrix, which indicates whether a given peak intensity above a threshold arises from the covariance of signals in the input spectra or whether it is likely to be caused by noise. Application to an unsymmetric covariance spectrum, obtained by concatenating two 2D 13 C-1 H heteronuclear, single quantum coherence ͑HSQC͒ and 13 C-1 H heteronuclear, multiple bond correlation ͑HMBC͒ spectra of a metabolite mixture along their common proton dimension, reveals that for sufficiently sensitive input spectra the reduction in sensitivity due to covariance processing is modest.

Fast and High‐Resolution Stereochemical Analysis by Nonuniform Sampling and Covariance Processing of Anisotropic Natural Abundance 2D 2H NMR Datasets

“…However, for nonlinear spectral estimates, such as covariance spectroscopy, the signal‐to‐noise ratio is no longer a reliable indicator of the sensitivity 67. 68 The assessment of sensitivity for NUS‐Cov is currently under investigation. Furthermore, the level of artifacts can be decreased by optimizing the NUS schedule.…”

Generalized Indirect Covariance NMR Formalism for Establishment of Multidimensional Spin Correlations

“…An important property of unsymmetric covariance NMR is that the sensitivity of the covariance spectrum is limited only by the sensitivity of the experiments it combines 16. For example, unsymmetric covariance of an 13 C- 1 H HMBC17 with a 13 C- 1 H HSQC spectrum establishes carbon-carbon correlations with the enhanced sensitivity characteristic of an inverse detected 13 C- 1 H heteronuclear spectra rather than that of a direct detected 13 C- 13 C correlation spectrum 4…”

A Covariance NMR Toolbox for MATLAB and OCTAVE

“…Invocation of the command [C C_axes] = covar(A, B, ‘axes1’, A_axes, ‘axes2’, B_axes, ‘power’, λ) performs the covariance transformation [A*B] λ (using the GIC notation described previously [12]) and, depending on the size of the resulting covariance spectrum, either stores that spectrum as a MATLAB array C (with the information required to write C out as an NMRPipe format file tabulated in C_axes ) or stores in C the name of a temporary file storing the covariance result as its singular value decomposition. Invocation of the command [C C_axes] = covar(A, B, ‘axes1’, A_axes, ‘axes2’, B_axes, ‘power’, λ, ‘Z’, 1 ) produces a Z-matrix [16] instead of an unscaled covariance spectrum. Invocation of covar with only a single spectrum provided performs symmetric covariance processing, either direct or indirect, depending on which dimension(s) are identified as donor dimensions.…”

“…Here we present a Covariance NMR Toolbox – compatible with both the MATLAB and the freely available OCTAVE computing environments – that implements all of the major covariance techniques, including direct covariance [8], indirect covariance [9], GIC [12] and the Z-matrix transform [xvi]. The Covariance NMR Toolbox, which is available via the MATLAB Central File Exchange (http://www.mathworks.com/matlabcentral/fileexchange/) or by request from the authors, reads and writes data in the well-documented and spectrometer independent NMRPipe [xvii] format and uses a small number of easy to use and extensible scripts to manipulate frequency domain data.…”