Development and Evaluation of Flexible Empirical Peak Functions for Processing Chromatographic Peaks

Abstract

This paper describes the results of developing and evaluating extremely flexible empirical peak-shaped functions for processing chromatographic peaks. The proposed peak functions were developed based on transformation of Gaussian function into two-step functions that separately describe the leading and trailing edges. The flexibility and capability of these models were achieved by the combination and empirical modifications of the leading and trailing edge functions. The flexibility of the models was evaluated by fitting them to 10 types of peak shapes generated by literature peak functions possessing asymmetry values from 1 to 2.8. Excellent fits were found between the proposed models and generated peak shapes, showing that the new peak functions are extremely flexible. Furthermore, the capability of the models to smooth noisy peaks was demonstrated by fitting them to noisy, exponentially modified Gaussian peaks with different noise levels (S/N ratio was ranged from 200 to 10). Finally, we conclude that the flexibility of these models can be used to establish "templates" to significantly aid in smoothing noisy peaks and peak deconvolution.

Cell separation mediated by differential rolling adhesion

“…In general, cell adhesion is very difficult to model, because chemical effects, such as receptor number, ligand density, and receptor-ligand affinity, are intimately tied to the physical effects of fluid forces, colloidal interactions, and cell deformability. However, the most important criterion for the suitability of a specific peak-shaped function is that, despite the lack of a rigorous physiochemical foundation, it should fit the experimental peaks well (Li, 1997). Our retention time distributions were fit very well by the EMG function, which is known to fit asymmetric and tailing peaks (Guiochon et al, 1994).…”

High-precision optical measurements of 13 C/ 12 C isotope ratios in organic compounds at natural abundance

“…Volumes of Ͼ25 L did not result in a significant improvement in the precision. Peaks are fit with an empirically transformed Gaussian function using a nonlinear least square curve fitting routine as described elsewhere (19). The repetition rate of 2 Hz limits the current setup to samples that pass through the instrument slowly relative to the few-second peak widths obtained using faster gas chromatography techniques.…”

Processing and classification of protein mass spectra

“…In order to describe such a broad peak the isotopic model may not be accurate, and more flexible approaches such as the ''exponentially modified Gaussian'' (Malmquist, 1994) or the very flexible ''empirically transformed Gaussian'' (Li, 1997) could be used. Shackmana, Watson, and Kennedy (2004) took the latter model to deconvolve overlapping peaks by means of nonlinear regression.…”

“…A real LC-MS signal consists of a sum of isolated signals plus noise and baseline where the noise has a different elution profile than peptides, which makes it possible to distinguish it from signals. Although the elution profile of a peptide is less well defined and less reproducible than its m/z signal, a Gaussian shape is usually a rather good approximation, but more flexible refinements were proposed (Malmquist, 1994;Li, 1997). Peak detection in the time domain is basically the same as peak detection in low-resolution mass spectra, and it can be done in a non-parametric or parametric way.…”