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. This involvement makes it critical to understand their structure-function relationships. Few system-independent, LC-MS/MS (Liquid chromatography tandem mass spectrometry) based studies have been developed with this particular goal, however. When studied, the employed methods generally rely on normalized retention times as well as m/z - mass to charge ratio of an 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 permethylated glycans derived from standard glycoproteins and human blood serum, using a Glucose Unit Index (GUI) as the reference frame in the space of compound parameters. For the reference frame we develop a closed-form analytic formula, which is obtained from 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 abstract manner which allows for immediate application to related physical and chemical processes. Results employing the proposed classification method are validated via comparison with experimental mass spectrometer data.

[1]  Haizhao Yang,et al.  Error bounds for deep ReLU networks using the Kolmogorov-Arnold superposition theorem , 2019, Neural Networks.

[2]  Steven L. Brunton,et al.  Data-driven discovery of partial differential equations , 2016, Science Advances.

[3]  Hao Xu,et al.  DL-PDE: Deep-learning based data-driven discovery of partial differential equations from discrete and noisy data , 2019, Communications in Computational Physics.

[4]  Yehia Mechref,et al.  Advances in mass spectrometry‐based glycomics , 2018, Electrophoresis.

[5]  Yehia Mechref,et al.  High-throughput solid-phase permethylation of glycans prior to mass spectrometry. , 2008, Rapid communications in mass spectrometry : RCM.

[6]  A. Varki.  Sialic acids in human health and disease. , 2008, Trends in molecular medicine.

[7]  Feng Xu,et al.  Data-driven Discovery of Partial Differential Equations for Multiple-Physics Electromagnetic Problem , 2019, 1910.13531.

[8]  Stephan Hoyer,et al.  Learning data-driven discretizations for partial differential equations , 2018, Proceedings of the National Academy of Sciences.

[9]  Y. Mechref,et al.  LC-MS/MS analysis of permethylated N-glycans facilitating isomeric characterization , 2016, Analytical and Bioanalytical Chemistry.

[10]  R. Contreras,et al.  Increased fucosylation and reduced branching of serum glycoprotein N-glycans in all known subtypes of congenital disorder of glycosylation I. , 2003, Glycobiology.

[11]  Joseph Sang-Il Kwon,et al.  Data-driven identification of interpretable reduced-order models using sparse regression , 2018, Comput. Chem. Eng..

[12]  J. Waals.  On the Theory of the Brownian Movement , 1918 .

[13]  Paulo Gonçalves,et al.  Empirical Mode Decompositions as Data-Driven Wavelet-like Expansions , 2004, Int. J. Wavelets Multiresolution Inf. Process..

[14]  S. Brunton,et al.  Discovering governing equations from data by sparse identification of nonlinear dynamical systems , 2015, Proceedings of the National Academy of Sciences.

[15]  Robert Gardner,et al.  Introduction To Real Analysis , 1994 .

[16]  George E. Karniadakis,et al.  Hidden physics models: Machine learning of nonlinear partial differential equations , 2017, J. Comput. Phys..

[17]  I. Gudelj,et al.  Protein N-Glycosylation in Cardiovascular Diseases and Related Risk Factors , 2018, Current Cardiovascular Risk Reports.

[18]  Kai Griebenow,et al.  Effects of glycosylation on the stability of protein pharmaceuticals. , 2009, Journal of pharmaceutical sciences.

[19]  Jun Li,et al.  Robust Low-Rank Discovery of Data-Driven Partial Differential Equations , 2020, AAAI.

[20]  André M Deelder,et al.  Mass spectrometry of proton adducts of fucosylated N-glycans: fucose transfer between antennae gives rise to misleading fragments. , 2006, Rapid communications in mass spectrometry : RCM.

[21]  Paris Perdikaris,et al.  Machine learning of linear differential equations using Gaussian processes , 2017, J. Comput. Phys..

[22]  Paris Perdikaris,et al.  Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations , 2017, ArXiv.

[23]  Joshua L. Padgett,et al.  The quenching of solutions to time-space fractional Kawarada problems , 2018, Comput. Math. Appl..

[24]  Pauline M Rudd,et al.  Glycans as cancer biomarkers. , 2012, Biochimica et biophysica acta.

[25]  Kaj Nyström,et al.  Data-driven discovery of PDEs in complex datasets , 2018, J. Comput. Phys..

[26]  Y. Mechref,et al.  Glycoprotein Enrichment Analytical Techniques: Advantages and Disadvantages. , 2017, Methods in enzymology.

[27]  Steven L. Brunton,et al.  Data-Driven Identification of Parametric Partial Differential Equations , 2018, SIAM J. Appl. Dyn. Syst..

[28]  J. Padgett,et al.  Anomalous diffusion in one-dimensional disordered systems: a discrete fractional Laplacian method , 2019, Journal of Physics A: Mathematical and Theoretical.

[29]  V. Tikhomirov.  On the Representation of Continuous Functions of Several Variables as Superpositions of Continuous Functions of one Variable and Addition , 1991 .

[30]  B. MacLean,et al.  Standardization of PGC-LC-MS-based glycomics for sample specific glycotyping. , 2019, The Analyst.

[31]  A. Einstein.  Zur Theorie der Brownschen Bewegung , 1906 .

[32]  J. Marth,et al.  Glycosylation in Cellular Mechanisms of Health and Disease , 2006, Cell.

[33]  D. Bilder,et al.  A Drosophila Tumor Suppressor Gene Prevents Tonic TNF Signaling through Receptor N-Glycosylation. , 2018, Developmental cell.

[34]  J. Padgett.  Analysis of an approximation to a fractional extension problem , 2019, BIT Numerical Mathematics.

[35]  Y. Mechref,et al.  N-Glycan Profile of Cerebrospinal Fluids from Alzheimer’s Disease Patients Using Liquid Chromatography with Mass Spectrometry , 2019, Journal of Proteome Research.

[36]  Y. Mechref,et al.  Analysis of Permethylated Glycan by Liquid Chromatography (LC) and Mass Spectrometry (MS). , 2017, Methods in molecular biology.

[37]  Bin Dong,et al.  PDE-Net: Learning PDEs from Data , 2017, ICML.

[38]  H. Schaeffer,et al.  Learning partial differential equations via data discovery and sparse optimization , 2017, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[39]  J. Hughes,et al.  Autosomal recessive phosphoglucomutase 3 (PGM3) mutations link glycosylation defects to atopy, immune deficiency, autoimmunity, and neurocognitive impairment. , 2014, The Journal of allergy and clinical immunology.

[40]  Paris Perdikaris,et al.  Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations , 2017, ArXiv.

[41]  Y. Mechref,et al.  Direct comparison of derivatization strategies for LC-MS/MS analysis of N-glycans. , 2017, The Analyst.

[42]  Y. Mechref,et al.  Isomeric Separation of Permethylated Glycans by Porous Graphitic Carbon (PGC)-LC-MS/MS at High Temperatures. , 2017, Analytical chemistry.

[43]  R. Dwek,et al.  "Internal residue loss": rearrangements occurring during the fragmentation of carbohydrates derivatized at the reducing terminus. , 2002, Analytical chemistry.

[44]  J. Padgett,et al.  Anomalous diffusion in semi-crystalline polymer structures , 2020, 2006.01068.

[45]  R L Stanfield,et al.  Roles for glycosylation of cell surface receptors involved in cellular immune recognition. , 1999, Journal of molecular biology.

[46]  Yehia Mechref,et al.  LC–MS/MS of permethylated N‐glycans derived from model and human blood serum glycoproteins , 2016, Electrophoresis.