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. K E Y W O R D Sdata-driven PDE, Einstein approach, learning algorithms INTRODUCTIONThe biological significance of glycans is evident from the numerous studies demonstrating their roles in living systems. These molecules alone, as well as in conjunction with other biomolecules, participate in important biological functions. For example, glycosylation is one of the major post-translational modifications 1,2 and is known to mediate a broad range of biological processes such as cell recognition, 3 cell signaling, 3,4 immune response, 5 and protein stability. 6 Furthermore, aberrations in glycosylation patterns are found to be related to various diseases, including cancers. 3,[7][8][9][10][11] Glycans display high structural complexity owing to the presence of diverse monosaccharide composition, different linkages, and various branching options. 12 Tandem mass spectrometry (MS) has emerged as an effective technique

MS‐based glycomics and glycoproteomics methods enabling isomeric characterization

“…High reproducibility of GUI values across different instruments and laboratories as well as different days was demonstrated. Most recently, Padgett et al (2021) used GUI as a reference frame and proposed a data‐driven partial differential equation model to classify unknown N‐ glycans using diffusivity and absorption.…”