Doubly indirect covariance

Zhang EL, Bruschweiler-Li L, Bruschweiler R (2010) Simultaneous de novo identification of molecules in chemical mixtures by doubly indirect covariance NMR spectroscopy. J Am Chem Soc 132(47) 16922-16927... 

Doubly indirect covariance (DIG) yields a symmetric correlation map [13]. It can further be considered as a bridge to the generalization of indirect covariance. It implies that correlation spectra, that are used for indirect covariance, themselves may be a creation of a previous covariance transformation. Scheme 5.1 serves as an example to elucidate this perspective. In Scheme 5.1A and B, indirect covariance generates homonuclear spectra. Part (C) leads to the creation of a heteronuclear correlation, which itself can be taken as component spectrum for transformation (A) or (B). It is apparent that Scheme 5.1 represents an oversimplification of the types of indirect covariance treatment. A wider variety of spectra that can be obtained by UIC processing is collected in Table 5.1. 

Scheme 5.1 Indirect covariance is sketched in (A), doubly indirect covariance (DIC) in (B) and unsymmetrical indirect covariance in (C). The powers of 14 and regularization factors have been omitted for simplicity. Common experimental abbreviations were used equivalent to the spectra or data matrices obtained from the corresponding experiment.

The two large-scale cormnercial vendors of spectrometer-independent NMR software currently offer covariance processing as a feature of their spectral manipulation and interpretation suites. The Spectrus platform by ADC/Labs and the MNova by Mestrelab Research provide stand-alone solutions that allow the import of all spectrometer data formats without the necessity of pre-processing. Covariance processing can be performed according to the direct, indirect, and generalized indirect formalism. The doubly indirect covariance transformation is formd in MNova. While... 

The appHcation of doubly indirect covariance was only described for a study on a metabolic model mixture consisting of isoleucine, carnitine. 

Covariance NMR has established itself as a valuable tool in the ranks ofNMR methodologies. As direct and indirect covariance of 2-dimensional NMR data sets, it can replace the second Fourier transformation, whereas as unsymmetrical and GIC it follows Fourier transformation. Based on matrix algebra and statistical mathematics, covariance transformations were extended to doubly indirect and 3- and 4-dimensional covariance NMR. Since the parent or component data arrays can originate from any type of 2D NMR experiment, 2D NMR spectra were co-processed to yield C-N and C-P correlations of non-isotopicaUy labelled small molecules. Further heterospectroscopic covariance was used to concatenate NMR and MS data allowing to allocate the information of both to a compound. 

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