Use of singular value decomposition analysis to differentiate phosphorylated precursors in strong cation exchange fractions

We studied the use of peak deviations (PDs) for application in phosphoproteomics. Due to the differences in the mass defects, the PDs of samples containing mixtures of phosphorylated and nonphosphorylated peptides show bimodal distributions. The ratios of peak heights accurately predict the phosphoproteome content of a sample. In this work, we apply a signal-processing tool, singular value decomposition, to reveal characteristic features of the phosphorylated, nonphosphorylated, and mixed samples. We show that a simple application of singular value decomposition to the PD matrix (i) detects transitions from mostly phosphorylated samples to mostly nonphosphorylated samples, (ii) reveals modes of low-abundance species in the presence of the high-abundance species (e.g., phosphorylated peptides), and (iii) simplifies the interpretation of the clustering of a covariance matrix obtained from PDs. As the eigenfunctions of the inner-product of the data matrix (made from the PDs) are Hermite functions, we observe a change of sign in the transition from samples enriched in phosphorylated peptides to samples containing fewer phosphorylated peptides. The ordering of the singular values of the data matrix points in the direction of changes to the phosphorylation content. No peptide identifications from a database were used for this study.