Bi-linear regression for ¹⁸O quantification: Modeling across the elution profile

Motivation: Interpreting and quantifying labeled mass-spectrometry data is complex and requires automated algorithms, particularly for large scale proteomic profiling. Here, we propose the use of bi-linear regression to quantify relative abundance across the elution profile in a unified model. The bi-linear regression model takes advantage of the fact that while peptides differ in overall abundance across the elution profile multiplicatively, the relative abundance between the mixed samples remains constant across the elution profile. We describe how to apply bi-linear regression models to ¹⁸O stable-isotope labeled data, which allows for the direct comparison of two samples simultaneously. Interpretation of model parameters is also discussed. The incorporation rate of the labeling isotope is estimated as part of the modeling process and can be used as a measure of data quality. Application is demonstrated in a controlled experiment as well as in a complex mixture. Results: Bi-linear regression models allow for more precise and accurate estimates of abundance, in comparison to methods that treat each spectrum independently, by taking into account the abundance of the molecule throughout the entire elution profile, with precision increased by one-to-two orders of magnitude.