A coherent mathematical characterization of isotope trace extraction, isotopic envelope extraction, and LC-MS correspondence.

Background: Liquid chromatography-mass spectrometry is a popular technique for high-throughput protein, lipid, and metabolite comparative analysis. Such statistical comparison of millions of data points requires the generation of an inter-run correspondence. Though many techniques for generating this correspondence exist, few if any, address certain well-known run-to-run LC-MS behaviors such as elution order swaps, unbounded retention time swaps, missing data, and significant differences in abundance. Moreover, not all extant correspondence methods leverage the rich discriminating information offered by isotope envelope extraction informed by isotope trace extraction. To date, no attempt has been made to create a formal generalization of extant algorithms for these problems.

Results: By enumerating extant objective functions for these problems, we elucidate discrepancies between known LC-MS data behavior and extant approaches. We propose novel objective functions that more closely model known LC-MS behavior.

Conclusions: Through instantiating the proposed objective functions in the form of novel algorithms, practitioners can more accurately capture the known behavior of isotope traces, isotopic envelopes, and replicate LC-MS data, ultimately providing for improved quantitative accuracy.