Regression analysis for comparing protein samples with ¹⁶O/ ¹⁸O stable-isotope labeled mass spectrometry

Motivation: Using stable isotopes in global proteome scans, labeled molecules from one sample are pooled with unlabeled molecules from another sample and subsequently subjected to mass-spectral analysis. Stable-isotope methodologies make use of the fact that identical molecules of different stable-isotope compositions are differentiated in a mass spectrometer and are represented in a mass spectrum as distinct isotopic clusters with a known mass shift. We describe two multivariable linear regression models for ¹⁶O/¹⁸O stable-isotope labeled data that jointly model pairs of resolved isotopic clusters from the same peptide and quantify the abundance present in each of the two biological samples while concurrently accounting for peptide-specific incorporation rates of the heavy isotope. The abundance measure for each peptide from the two biological samples is then used in down-stream statistical analyses, e.g. differential expression analysis. Because the multivariable regression models are able to correct for the abundance of the labeled peptide that appear as an unlabeled peptide due to the inability to exchange the natural C-terminal oxygen for the heavy isotope, they are particularly advantageous for a two-step digestion/labeling procedure. We discuss how estimates from the regression model are used to quantify the variability of the estimated abundance measures for the paired samples. Although discussed in the context of ¹⁶O/¹⁸O stable-isotope labeled data, the multivariable regression models are generalizable to other stable-isotope labeled technologies.