Mathematical chromatography deciphers the molecular fingerprints of dissolved organic matter.

High-resolution mass spectrometry (HRMS) elucidates the molecular composition of dissolved organic matter (DOM) through the unequivocal assignment of molecular formulas. When HRMS is used as a detector coupled to high performance liquid chromatography (HPLC), the molecular fingerprints of DOM are further augmented. However, the identification of eluting compounds remains impossible when DOM chromatograms consist of unresolved humps. Here, we utilized the concept of mathematical chromatography to achieve information reduction and feature extraction. Parallel Factor Analysis (PARAFAC) was applied to a dataset describing the reverse-phase separation of DOM in headwater streams located in southeast Sweden. A dataset consisting of 1355 molecular formulas and 7178 mass spectra was reduced to five components that described 96.89% of the data. Each component summarized the distinct chromatographic elution of molecular formulas with different polarity. Component scores represented the abundance of the identified HPLC features in each sample. Using this chemometric approach allowed the identification of common patterns in HPLC-HRMS datasets by reducing thousands of mass spectra to only a few statistical components. Unlike in principal component analysis (PCA), components closely followed the analytical principles of HPLC-HRMS and therefore represented more realistic pools of DOM. This approach provides a wealth of new opportunities for unravelling the composition of complex mixtures in natural and engineered systems.