A time-domain algorithm for NMR spectral normalization.

Abstract

Recently, a new method for quantitatively comparing NMR spectra of control and treated samples, in order to examine the possible occurring variations in cell metabolism and/or structure in response to numerous physical, chemical, and biological agents, was proposed. This method is based upon the utilization of the maximum superposition normalization algorithm (MaSNAl) operative in the frequency domain and based upon maximizing, by an opportune sign variable measure, the spectral region in which control and treated spectra are superimposed. Although the frequency-domain MaSNAl algorithm was very precise in normalizing spectra, it showed some limitations in relation to the signal-to-noise ratio and to the degree of diversity of the two spectra being analyzed. In particular, it can rarely be applied to spectra with a small number of visible signals not buried in the noise such as generally in vivo spectra. In this paper, a time-domain normalization algorithm is presented. Specifically, it consists in minimizing the rank of a Hankel matrix constructed with the difference of the two free induction decay signals. The algorithm, denoted MiRaNAl (minimum rank normalization algorithm), was tested by Monte Carlo simulations as well as experimentally by comparing two samples of known contents both with the new algorithms and with an older method using a standard. Finally, the algorithm was applied to real spectra of cell samples showing how it can be used to obtain qualitative and quantitative biological information.