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

Abstract

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.