Figure 1

¹⁸O/¹⁶O labeling problem setting. To quantitatively compare peptides their C-term is ideally labeled with heavy oxygen (two ¹⁸O) or light oxygen (two ¹⁶O), but partial labeling also occurs (mixed). These isotope species give rise to overlapping isotopic contours with individual contributions (a, b and c) to the observed MS spectra peaks. The input data used for the data analysis were nine observed spectral intensities (S₀-S₈) including possible missing values. These intensities () are assumed to equal a weighted sum of three isotope contours (Peptide C-terms: Light (¹⁶O₂), Mixed (¹⁸O, ¹⁶O) and Heavy (¹⁸O₂)), a constant background K_bg and an error term ε. The weights (a, b and c) are of particular interest since they describe the contribution of unlabelled (Light:a) and labeled (Mixed:b and Heavy:c) isotopes. In the theoretical case where the background constant and error term are removed a theoretical framework is presented (see Table 1), where the above experiment is performed twice for each peptide with swapped labels (i.e. Direct and Inverted experiments).