Object classification in analytical chemistry via data‐driven discovery of partial differential equations

Glycans are one of the most widely investigated biomolecules, due to their roles in numerous vital biological processes. However, few system‐independent, LC‐MS/MS (liquid chromatography tandem mass spectrometry) based studies have been developed with this particular goal. Standard approaches generally rely on normalized retention times as well as m/z‐mass to charge ratios of ion values. Due to these limitations, there is need for quantitative characterization methods which can be used independently of m/z values, thus utilizing only normalized retention times. As such, the primary goal of this article is to construct an LC‐MS/MS based classification of the glycans derived from standard glycoproteins and human blood serum using a glucose unit index as the reference frame in the space of compound parameters. For the reference frame, we develop a closed‐form analytic formula via the Green's function of a relevant convection‐diffusion‐absorption equation used to model composite material transport. The aforementioned equation is derived from an Einstein–Brownian motion paradigm, which provides a physical interpretation of the time‐dependence at the point of observation for molecular transport in the experiment. The necessary coefficients are determined via a data‐driven learning procedure. The methodology is presented in an abstractly and validated via comparison with experimental mass spectrometer data.